Bring a large pot of water to a boil. Season the water with salt and cook rigatoni to al dente.
Remove the casing from the sausage links. Add the sausage to a large skillet over medium heat. Break into chunks with a wooden spoon. After a minute, add the garlic. Saute until sausage is cooked. About 4 minutes.
Add broccolini to the sausage and garlic and season with a pinch of salt and pepper. Place a lid on the skillet and cook for 5 minutes, stirring occasionally.
Add vegetable stock to deglaze the pan, then add lemon zest and crushed red pepper flake and lemon juice.
Add cooked pasta to the pan and cook everything together until most of the liquid from the pan has mostly evaporated. Serve.