Bring a large pot of water to a boil. In a large nonstick skillet, warm oil over medium-high heat. Cook sausage, stirring and breaking up lumps, until golden brown, about 3 minutes. Add onion, rosemary and 1/2 tsp. salt. Reduce heat to medium and cook, stirring, until tender, about 3 minutes. Stir in broccoli rabe, garlic and red pepper flakes and sauté until broccoli rabe is tender, 5 to 8 minutes, adding broccoli rabe by handfuls if skillet is too full. Remove skillet from heat.
Add 1 tsp. salt and pasta to boiling water. Stir and cook until pasta is al dente, about 10 minutes or according to package directions. Reserve 1/2 cup cooking water; drain pasta.
Add broth, 1/4 cup cheese, pasta and cooking water to skillet. Cook over medium heat until liquid has reduced and coats pasta, about 3 minutes. Divide pasta among bowls, sprinkle with remaining 1/4 cup cheese and additional red pepper flakes, if desired, and serve.