Peel and wash the carrots and cut them into thin strips with a peeler. Clean, wash and cut the leek lengthwise into thin strips. Peel and wash celery and cut into fine sticks.
Cook the pasta in plenty of boiling salted water for 9-11 minutes. After 4-5 minutes add vegetables. Melt the fat in a saucepan. Dust with flour and sauté briefly while stirring. Stir in milk and stock bit by bit.
Grate the cheese and gradually stir into the béchamel sauce. Wash the parsley, dab dry, pluck the leaves from the stalks and chop coarsely. Stir the parsley into the béchamel sauce. Drain the pasta and vegetables and serve with the cheese béchamel.