Clean and rinse Brussels sprouts, perhaps cut in half. Cook in boiling salted water for about 20 minutes.
Cook pasta in really boiling hot salted water for about 10 min. al dente.
In the meantime, cut meat sausage into slices and cut the slices in half. Grate cheese. Drain the pasta and cool. Drain Brussels sprouts, reserving vegetable water.
Finely dice onion and sauté in hot fat. Sprinkle with flour and sauté. Extinguish with milk and Brussels sprouts water. Simmer for 5 minutes at low temperature. Fold in a good half of the cheese and season the sauce with salt and pepper.
Place the pasta, Brussels sprouts and sausage in a gratin dish and pour the cheese and béchamel sauce over them. Sprinkle with the remaining cheese and bake in the heated oven for about 35 minutes. Chop the parsley and sprinkle over the casserole. Garnish with parsley fronds if desired.