Bring a large pot of water to the boil, add 1 small handful kosher salt and the rapini (see notes below if using stalks). Cook 3-4 minutes then lift the rapini out of the water with tongs and set aside. Reserve the cooking water for the pasta.
Place sausage in a large skillet over medium-high heat. Cook, stirring and crumbling, until browned, 5 to 8 minutes. Using a slotted spoon, transfer sausage to a bowl and drain excess fat from pan.
In the same skillet, warm the extra virgin olive oil over medium heat. Add the garlic and red pepper flakes and cook until fragrant and garlic just begins to brown. Add the rapini and continue cooking on low until rapini becomes very tender.
Meanwhile, bring the water back to a boil, add the pasta and cook until al dente. Using tongs, lift the cooked pasta, and the residual water that clings to it, and transfer it to the frying pan. Reserve 1/2 cup pasta water.
Return sausage to the skillet and stir to combine entire mixture. Season with salt and pepper to taste, adding some of the pasta water if mixture seems too dry; sprinkle with cheese and serve immediately.
Notes
Buy only very fresh rapini with leaves and buds that are crispy and vibrant green, not dry-looking or yellowed. The stalks should not be mushy or browned. *You can skip this step and simply discard the thick stems, but much like broccoli, the thicker stalks are meant to be eaten. Trim the ends then peel the long stalks. Once peeled, cut about 2 inches of the peeled stems off the stalk and boil for a minute or two before adding the florets to the salted water. Continue to cook stems and tops together for 3-4 minutes until tender. Proceed with recipe.