1. Bring a large pot of water to a boil.
2. Heat oil in a Dutch oven over medium-high heat. Add sausage and saute, breaking up large chunks with a wooden spoon, until lightly browned, about 5 minutes. Add garlic and crushed red pepper; cook, stirring, 30 seconds. Add broccoli rabe and cook, tossing with tongs, 1 minute. Add broth, reduce heat to medium, cover and cook until broccoli rabe is tender, about 3 minutes.
3. Cook pasta according to package directions, then drain and add to sausage mixture; toss well with tongs. Add 1/4 cup cheese and black pepper and toss well again. Divide among four bowls and sprinkle with remaining cheese.