Get a large pot of salted water to boil.
Parboil the broccoli rabe: Toss the chopped broccoli rabe into the pot of boiling water and let it cook for 2 minutes. Take the parboiled broccoli rabe out of the pot with a slotted spoon or spider and set it aside
Let the pot of water return to a boil and add the orecchiette. Let the pasta cook in the water until al dente.
Make the base for the sauce: While the pasta is cooking get out a walled skillet or pan and add the olive oil to it. Place it over medium-high heat, toss in the sausage, and use a spoon to break up the sausage into medium-sized crumbles. Saute the sausage until fully cooked and slightly browned, about 5 to 6 minutes. Next, toss in the minced garlic and crushed red pepper, and continue to sautee everything for another 30 seconds. Finally, toss in the parboiled broccoli rabe and stir so that it is incorporated in with the other ingredients. Lower the heat while you wait for the orecchiette to finish cooking.
Finish the dish: Remove the al dente orecchiette from the pot with a slotted spoon/spider and transfer to the skillet/pan. Use a ladle to add about 1 cup of the pasta water to the skillet/pan. Raise the heat and stir all of the ingredients together until the pasta water thickens up and coats everything, about 2 to 3 minutes. Remove the skillet/pan from the heat, toss in the cheese, and stir until the cheese melts and coats everything. Finally taste the pasta and add salt and pepper to your liking.
Transfer the pasta to plates, top with some extra cheese, and enjoy immediately.