Bring a large pot of salted water to a boil. Add orecchiette and boil until al dente according to package instructions, 10 to 12 minutes. Drain orecchiette, reserving about half a cup of pasta cooking water, and transfer to a bowl with sausage.
Meanwhile, heat a large skillet over medium. Add sausage and cook until browned, breaking sausage up with a wooden spoon so it browns evenly, 8 to 10 minutes. Remove sausage from skillet and transfer to a large bowl; leave drippings in skillet.
Add olive oil to skillet, keeping heat at medium. Add broccoli rabe to pan and cook until wilted and starting to brown, about 5 minutes. Season broccoli rabe with salt and add garlic. Cook garlic, stirring frequently, until fragrant but not browned, about 2 minutes.
Transfer broccoli rabe and garlic to the bowl with the pasta and sausage and toss to combine with reserved pasta water.
Divide the pasta among 4 bowls, top it with shaved Parmesan and crushed red pepper flakes, and serve.
