Place sausage in a large skillet over medium heat and, using a wooden spoon, cook until brown and crumbly.
Meanwhile, bring at least 4 quarts of lightly salted water to boil and add broccoli rabe and cavatelli. Cook until pasta is done, approximately 11 minutes. Before draining, reserve approximately 2 cups of pasta cooking water.
When sausage is done, remove from skillet with a slotted spoon. Add extra virgin olive oil to skillet drippings and cook over medium heat until warm. Add sliced garlic, and red pepper flakes and cook until lightly golden (about 1 minute). Add about 1 cup of pasta cooking water to skillet and cook for 1 minute more. Then add drained pasta and broccoli rabe to skillet. Stir to combine and add reserved sausage. Add salt, pepper, and cheese to taste. Stir to combine again. Simmer for 2 minutes or so. If too thick, add more of the reserved pasta cooking water until desired consistency.