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.

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.

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.