Bring a large pot of salted water to a boil. Add the orecchiette and cook according the the package directions. Before you drain the orecchiette, scoop out 1 - 1 1/2 cups of pasta water and set it aside.
Meanwhile, heat 1 tablespoon of the olive oil in a heavy 12-inch skillet over medium high heat. Once the oil is shimmery, add the sausage, breaking it up as you cook it. When you're done the sausage will be golden to deep brown, in bite sized pieces, and fully cooked through. This will take 12-15 minutes. Transfer the cooked sausage to a bowl.
Add the broccoli rabe along with 2 tablespoons of water to the skillet. Cover the skillet and let it steam for about 2 minutes. Then uncover the skillet, add 1 tablespoon of olive oil, and saute the broccoli rabe until it is browned and tender. Add the garlic to the skillet, give it a stir and take the skillet off the heat while the pasta finishes cooking.
Once the pasta is done, put the skillet on medium high. Add the sausage back to the skillet and then add the pasta. Pour in about 1 cup of the pasta water and cook everything until the sauce is thickened, 1-2 minutes. Stir in the remaining 1 tablespoon of olive oil and sprinkle in the basil and red pepper flakes. Serve with shavings of parmesan over the top.