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Bring a large pot of water to a rolling boil over high heat. Halve and core the cabbage, then thinly shred.
In a large saucepan or large, deep skillet, add the butter and melt over medium heat. Add the cabbage, salt, red pepper (if using) and black pepper. Cook, stirring often, for about 20 minutes, or until the cabbage has cooked down significantly and is deeply caramelized. If it becomes too dry as it cooks, add a splash or two of the pasta water to prevent it from sticking and to deglaze the pan.
Meanwhile, once the pasta water reaches a boil, salt generously and add the pasta. Cook until al dente. Reserve about 1 cup of pasta water, then drain.
Add the cooked pasta to the saucepan with the cabbage along with the parm and about ½ cup of reserved pasta water. Reduce the heat to low, and cook, stirring constantly, until the pasta is creamy and the cheese has melted. Add a little more pasta water as needed to create a creamy sauce. Remove from the heat and garnish with fresh parsley (if desired) before serving.
Refrigerate leftovers in an airtight storage container for 4 days. Add a splash of water before reheating to help loosen the sauce.