• Sift together the flour, cocoa, and baking soda.
  
• In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the butter and both sugars together on medium speed until fluffy, light, and creamy, about 3 minutes. Add the salt and vanilla and beat to combine. Turn off the mixer, add all the dry ingredients and start mixing on the lowest setting to prevent flour from flying everywhere. Turn the mixer up a few notches, and mix until the dough forms big, moist curds. Add the chopped chocolate pieces and mix to incorporate. 
• Turn the dough out onto a work surface (I turned it out directly onto a sheet of plastic wrap) and gather it together, kneading it if necessary to bring it together. Divide the dough in half. Shape the dough into logs that are about 1 1/2 inches in diameter by 9 inches in length. Wrap the logs in plastic wrap and freeze them for at least 2 hours or refrigerate them for at least 3 hours.

  Note: The dough can be refrigerated for up to 3 days or frozen for up to 2 months. If you’ve frozen the dough, you don't need to defrost it before baking; just bake the cookies 1 minute longer.
• To Bake: Preheat oven to 325°F and place racks in center of oven or away from any known hot spots. Line two baking sheets with parchment paper or silicone baking mats.
• Using a long, sharp knife, slice each log of dough into 1/2-inch-thick rounds. If the rounds crack as you’re cutting them, just squeeze the broken pieces back together. Place the rounds on the baking sheets, leaving about 2 inches between them. If you need to bake in two batches, refrigerate the remaining cookies until you're ready to bake.
• Bake the cookies for 12 minutes. Don’t open the oven, just let them bake. When time is up, the cookies won’t look done, and will still be soft. Let the cookies cool on the baking sheet for about 1 minute until they've firmed up slightly, then use a spatula to transfer the cookies to a cooling rack. Eat the cookies warm, or at room temperature (the texture is arguably more interesting at room temperature).

For the cake:

• Place oven rack in lower-middle position and preheat oven to 350°F. Line two 8-inch cake pans with parchment paper and grease with butter or nonstick spray. 
• Combine butter and coffee in a large (5-quart) stainless steel pot, and set over low heat, stirring occasionally. After the butter has fully melted, remove from heat and whisk in the cocoa and chocolate. Stir until the chocolate has fully melted, then stir in the brown sugar, vanilla, and salt. Add the eggs and the yolks, and stir to combine. Sift in the flour and baking soda. Whisk thoroughly to mix, then divide evenly among the prepared cake pans (there will be about 23 ounces of batter in each pan if you're using a kitchen scale).
• Bake at 350°F for 25-30 minutes, or until a toothpick inserted into the center of the cakes comes out mostly clean with a few crumbs still attached. Cool in the cake pans for about 15 minutes, then remove the cakes from the pans. Peeling off the parchment, cool on a wire rack until no warmth remains, about 1 hour.

For the frosting:

• Fill a wide pot with 1-2 inches of water, and heat until gently simmering. Combine egg whites, sugar, salt, and cream of tartar in the bowl of a stand mixer, or a stainless steel bowl if using a hand mixer. Place the bowl over the pot of simmering water. Make sure the bottom of the bowl does not touch the water. If it does, place a thick ring of crumpled tinfoil on the bottom of the pot to act as a "booster seat" to raise the bowl up.
• Heat egg white mixture over the simmering water, whisking constantly, until mixture reaches 185°F (85°C). This will take about 10 to 12 minutes; if the mixture is heating slowly, turn up the heat. Once ready, remove from heat and transfer to a stand mixer fitted with a whisk attachment. Whip at high speed for about 10 minutes, until meringue is shiny, stiff, and cool to the touch, around 90°F (32°C).
• With the mixer switched to low, add butter, 1 or 2 tablespoons at a time. Make sure that the butter is close to room temperature to best incorporate with the meringue. After all the butter has been added, the buttercream should be thick, creamy, and soft but not runny, around 72°F (22°C). Add vanilla extract and mix on low speed until combined.
• Melt chocolate, either in a microwave or over a water bath (I did it in the microwave, in 20-second increments, stirring after each increment, until it was fluid and completely melted). You can play around with the amount of chocolate you add - the lower end of the suggested quantity range will produce a "milk" chocolate profile, and additional chocolate will produce incrementally deeper chocolate flavor (I used about 7 ounces, or a little less than 1 1/2 cups).
• Add all of the warm chocolate into the mixer bowl at once, then immediately begin whipping on medium-high speed until fully incorporated. Scrape bowl with a flexible spatula, then mix again for a few minutes until light, creamy, and silky smooth. If desired, adjust to taste with additional salt, vanilla, or melted chocolate.

Assembly:

• Trim the domed tops from the cakes with a serrated knife (they don't have to be perfectly level, just free from major lumps). Place one layer on a serving plate, cut side up. Cover the top with about 1 cup of frosting. Place the second cake layer on top of the frosting cut side down (this will help to reduce crumbs on the top of the cake). Spread a thin layer of frosting all over the cake to make a smooth foundation and trap any crumbs. Refrigerate for 10-15 minutes to set the crumb coat, then cover the cake with the remaining frosting.

To make the caramel-vanilla peanut brittle:

• Combine the water, corn syrup, sugar, and butter in a 3-quart stainless steel pot. Split the vanilla bean lengthwise with a paring knife and scrape out the seeds, adding the seeds to the pot. Place the pot over medium-low heat and cook, gently stirring until the syrup is bubbling vigorously around the edges, about 5 minutes. Raise the heat to medium-high, clip on a candy thermometer if you like, and cook, without stirring, until the syrup is golden brown, about 10 minutes (or approximately 340°F). I didn't find it was necessary to use a thermometer - once the syrup starts to brown, it will be ready in a couple of minutes, so keep an eye on it. The edges of the syrup may brown quicker than the middle - if this happens, you can swirl the pot to distribute the sugar. The syrup will be ready when it is the color of smooth peanut butter - put a can next to the stove to compare.
• While the sugar is cooking, mix together the baking soda and salt and have it ready to go by the stove. Grease an aluminum baking sheet, or put down a piece of parchment paper. 
• When the syrup is golden brown, turn off the heat, remove the thermometer (if using), and stir in the baking soda and salt with a heat-resistant spatula. Be careful - the syrup will be incredibly hot! Stir in the peanuts, then scrape the mixture onto the prepared baking sheet and spread into a roughly 12-by-8-inch layer. Don't worry if you end up with large clumps of peanuts stuck together - you can break them apart later if you like. Cool to room temperature, about 1 hour.
• Chop or break the brittle into 2-inch pieces. And, voila! Wasn't that easy? Now you have delicious caramel-vanilla peanut brittle that is an amazing candy in and of itself. Store half of the brittle in an airtight container - it will keep for about a month at room temperature, or up to 6 months in the freezer.

Now getting on to the peanut butter cups:

• Coarsely chop the remaining half of the peanut brittle. Put the pieces in a food processor and pulse until the pieces break down into a loose powder. Add the peanut butter, vanilla, and salt and grind to a smooth paste, about 2 minutes. It will start off looking like a ball of dough, but keep the processor going until the paste loosens and smooths out into a thick but spreadable consistency. Stella Parks recommends you transfer the filling to a piping bag fitted with a 1/2-inch plain tip, but I didn't have one and just placed the filling in a bowl and dolloped it onto the cups with a spoon. This also worked fine, although maybe piping it would ensure a more even and consistent layer of filling. I give instructions for both methods later.
• Temper the chocolate. Coarsely chop about 2/3 of the chocolate into 1/4-inch cubes, and place into a stainless steel bowl. Finely chop the rest of the chocolate and set aside. Heat a saucepan containing about an inch of water over medium-low heat until the water is just barely simmering. Place the metal bowl with the chocolate on top of the saucepan to create a double boiler, making sure that the bottom of the bowl doesn't touch the water. Stir the chocolate to melt it, while monitoring the temperature with a digital thermometer - do not let the temperature get above 105°F. If the temperature is rising too rapidly, take the chocolate off the heat for a few seconds and stir to release heat. When the chocolate is completed melted and just shy of 105°F, about 8-10 minutes, take it off the heat and stir in about 1/3 of the finely chopped chocolate. Stir until all the chocolate has melted, and then add in the remainder of the finely chopped chocolate, except for about 1/4 cup - save this 1/4 for emergency use. Stir for 5 minutes, until all the chocolate has melted (keep stirring even if the chocolate melts before the 5 minutes - this is necessary to properly agitate the chocolate). After stirring, the goal is to have the chocolate be at 84-86°F - it is now ready for use! If the chocolate cools too quickly and becomes thick, place the bowl over the hot water bath for 5 seconds, then stir vigorously off heat.

  Notes: To test the chocolate, dip a butter knife into the chocolate and refrigerate for two minutes. If it comes out soft or melts to the touch, it hasn't tempered correctly, and your best bet is to repeat the whole process. If it comes out streaked or swirled but semi-firm or slightly tacky, it needs to be agitated more - stir vigorously for two more minutes, and test again. If it comes out hard, glossy, and snappy, it's tempered and your chocolate is ready for use!

  During use, if the chocolate cools and becomes too thick, carefully rewarm it by setting it over the water bath for a few seconds, then stirring off heat. However, do not let the chocolate exceed 86°F - if it accidentally overheats, immediately add the "emergency" chocolate and stir like mad.
• Assemble the peanut butter cups. Line muffin pans with fluted cupcake papers. I found it helpful to make the cups in batches of 6 or 12. Drop a tablespoon of chocolate into the cupcake papers. Add the peanut butter filling one of two ways: 1) With the piping bag, hold it vertically, perpendicular to the layer of chocolate, and pipe about 1 tablespoon of filling into the center of the chocolate. 2) Using a spoon, gently drop about 1 tablespoon of filling into the center of the chocolate. In either case, dropping the peanut butter filling should push the chocolate up the sides of the paper. Top each cup with another tablespoon of chocolate, smoothing the tops if necessary with an offset spatula. Lightly tap the pan on the counter a few times to even and smooth out the tops further. Refrigerate until the chocolate is set, about 30 minutes. Repeat with remaining cupcake papers, chocolate, and peanut butter filling.