Bring a large pot of salty water to boil. Meanwhile, thinly slice 3 garlic cloves, remove and discard the casings from 4 sausages and roughly chop enough rapini to fill 4 cups.
Heat a large sauce pan on medium-low heat. Once hot, add enough oil to generously coat the bottom of the pan (about 3-4 tbsp). Add sliced garlic and let sizzle until your kitchen smells garlicky, about 2 minutes.
Break up the sausage meat into bite-sized pieces and transfer to the pan. Let brown on one side, about 5 minutes, then flip and use a wooden spoon to break the sausage into smaller, dime-sized pieces. Let cook until ⅓ of the meat is brown and caramelized.
By now your water should be boiling. Add pasta and cook to al dente by following package instructions. In the last 3 minutes of pasta cook time, add chopped rapini and let cook until the rapini is bright green and the pasta is cooked. Once done, reserve 2 cups of water and drain the rest.
Back in the pan, add 1 tbsp chili flakes and a pinch of salt, then deglaze with 3 tbsp sherry vinegar. Scrape the bottom of the pan with your spoon to release any brown bits stuck at the bottom. Turn heat to low and let it hangout while the pasta finishes.
Transfer the cooked pasta and rapini to the pan. Add ½ cup pasta water and stir on low heat. Stir in parmesan, adding more pasta water as needed until a glossy sauce coats every noodle. Finish with fresh cracked black pepper.
