Cook the pasta according to the package directions. Drain and return it to the pot.
Meanwhile, heat the oil in a large saucepan over medium heat. Add the sausage and cook, breaking it up with a spoon, until it’s no longer pink, 5 to 6 minutes.
Stir in the garlic and cook 1 minute.
Add the broth and red pepper and bring to a boil. Add the broccoli rabe and simmer, covered, until tender, 3 to 4 minutes.
Stir in the butter and Parmesan and cook, uncovered, until the sauce thickens slightly, 1 to 2 minutes.
Toss the pasta with the sausage mixture and ¼ teaspoon each salt and pepper.