Boil the pasta in salted water in another saucepan. Before the end of cooking, pour in the broccoli. When cooked, strain everything.
Heat the oil in a frying pan, add the chopped onion and garlic and cook until it starts to get soft (about 2 minutes). Then add the sliced cooked sausages, and continue cooking until the sausages are browned.
Stir in the pasta with the broccoli, keep cooking while stirring for another minute, then season with salt and pepper. Before serving, sprinkle with the grated hard cheese.
