Bring a large pot of salted water to a boil. Add the broccoli rabe and cook until crispy-tender, about 3 minutes. Remove the broccoli rabe with a slotted spoon and set aside.
Bring the water back to a boil and cook pasta according to the package instructions. Drain, reserving 1/2-cup of hot pasta water and set aside.
Meanwhile, heat the oil over medium heat in a large skillet. Add the sausage and cook, breaking it up with a spoon until browned, about 8 minutes. Add the garlic and red pepper flakes and sauté until fragrant, about 1 minute.
Add the broccoli rabe and toss to coat. Add 1/4-cup of the reserved pasta water and 1 tablespoon of oil and stir unti a creamy sauce forms.
Ad the pasta and toss well. If the pasta seems dry, add the remaining pasta water. Remove the pan from heat, stir in the Parmigiana Reggiano and serve.