Place a large pot of heavily salted water on the stove to boil. If it boils before you're ready to cook the pasta, just turn the heat off and cover the pot. This will keep your water piping hot and ensure that it starts boiling almost immediately after you turn the heat back on.

Heat the oil in a very large skillet or Dutch oven over medium-low heat. Add about half of the garlic and cook until fragrant, about 1 minute. Add the chile flakes and cook for about 30 seconds more. Stir in the cabbage and the salt - it will feel like too much cabbage, but it will cook down, don't worry. Cover and cook for about 10 minutes over medium-low heat, stirring occasionally. Uncover and turn the heat up to medium-high. Cook until the cabbage caramelizes. Stir occasionally at first, then more frequently once the cabbage starts caramelizing to prevent burning. Don't worry if cabbage pieces start sticking to the pan - just keep scraping the bottom of the pan and tossing the mixture around. Depending on a whole host of factors (how much cabbage you use, how wide your pot is, how much water was in the cabbage when you started), the caramelization process will take anywhere from 10 - 30 minutes after uncovering the pot. Be patient, and let color and taste be your guide. The cabbage should take on a light golden brown color, and be sweet and flavorful. It will be completely softened, and will have reduced dramatically in volume.

While you're waiting for the cabbage, melt the butter in a separate small skillet over medium heat. Add the anchovies and cook, mashing with a spatula, until they dissolve into the butter. Stir in the remaining garlic and cook until fragrant, about 1 minute. Stir in the bread crumbs, sage, and capers, if using, and cook until the mixture is brown and crispy, about 2 minutes. Season with black pepper and set aside.

When the cabbage is just starting to turn brown at the edges, add the pasta to the boiling pot of water and cook according to package instructions until barely al dente. Drain.

Add the pasta and bread-crumb mixture into the cabbage mixture and combine, heating everything through. Remove the pan from heat, add in the cheese and toss to combine. Season with salt and lots of freshly cracked black pepper, if desired.