Cook the pasta according to the package directions. Meanwhile, in a large saucepan, over medium heat, heat the oil. Add the sausage and cook, crumbling it with a spoon, until browned, about 5 minutes. Add the garlic and cook for 1 minute more. Add the broth and red pepper and bring to a boil. Then add the broccoli rabe, cover, and cook until tender, about 3 minutes. Stir in the butter and Parmesan and cook, uncovered, until the sauce thickens slightly, about 2 minutes. Add the drained pasta, season with the salt and black pepper, and toss to combine.
Tip: Broccoli rabe, a leafy distant cousin of broccoli, has a bitter flavor and smaller florets. For a milder alternative, substitute broccoli. For a more peppery bite, try arugula, Swiss chard, or beet greens.