Boil a big pot of salted water. Blanch the rapini for 3-5 minutes, until mostly tender. Remove the rapini and cook the pasta in the same water to save a pot.
Brown an Italian sausage in some olive oil, and break it up into small pieces. I use a spoon to smush it flat, and then I chop it with the edge of a wooden spatula. Add a couple cloves of chopped garlic and a dash of hot pepper flakes.
Right when the garlic starts to brown, add a glug of white wine or Vermouth. Then add half a can of chicken broth. When the pasta is nearly done, add the rapini and thicken the sauce with a bit of cornstarch (approx 1 T) dissolved in cold broth or water: