Cook the pasta in boiling salted water for 10-12 minutes. Cook vegetables in the broth for 5 minutes and remove with a skimmer. Heat the fat in a saucepan. Sweat flour in it and deglaze with milk and vegetable stock.
Bring to the boil while stirring. Season to taste with salt and pepper. Skin the sausage, dice it and add it to the sauce with the vegetables. Wash parsley, chop finely except for a few stalks. Drain noodles, rinse briefly with hot water and arrange on plates.
Pour vegetable sauce over it and sprinkle with parsley and garnish.