Heat a large sauté pan over medium heat. Add the oil and sausage and cook until browned. Stir in the garlic and cook for 1-2 minutes more so the sausage begins to caramelize. Add the cabbage and chicken broth, season with salt and pepper and cook until the cabbage has wilted, 5-7 minutes.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions.
Drain the pasta and add it to the sauté pan, saving some pasta cooking water. Stir in the cheese and parsley, and season with salt and pepper to taste. Stir in red pepper flakes, if using. Add pasta cooking water as needed.
Serve and top with more parmesan cheese if desired.