Prepare ingredients: Remove casings from sausages. Mince garlic. Trim and wash rapini, removing any tough stalks. Set aside.
Bring large pot of water to boil. Add salt and pasta and cook according to instructions.
While pasta is cooking, bring large non-stick skillet to medium-high heat. Add two tablespoons (roughly) of extra virgin olive oil. Add sausage (without casings). garlic, and red hot pepper flakes. Using wooden spoon, slowly break apart meat until in bite-size pieces, cooking until just pink.
Add rapini and pasta water. Bring heat to low. Cover pan and allow greens to steam slightly. Remove cover and allow mixture to cook slowly on low heat, allowing pasta water to evaporate slightly.
Drain pasta in colander and immediately add to skillet. Turn off heat and slowly stir until comes together.
Serve and garnish with shaved Parmigiano-Reggiano cheese.