Trim the French beans, remove any filaments and cut them in small bits. Trim, peel and cut the carrots into rounds and then wash. In a saucepan of boiling salted water blanch the carrots and the French beans for about 3 minutes. Then drain and set aside. Peel and cut the onion; peel the garlic, wash the parsley and mince them together.Trim the aubergine, then wash it and cut it into small cubes place in a colander, sprinkle with salt and drain about 20 minutes to allow them to give out their own water. In a saucepan with oil fry the onion, part of the parsley and the garlic until soft but not golden. Add the drained aubergine cubes, the carrots and the French beans; brown for 3 minutes, stirring with a wooden spoon.Add the tomatoes, a pinch of salt and pepper and cook for another 20 minutes over a moderate heat. Before removing the sauce from the heat, add the remaining parsley and garlic. In the meanwhile cook the pasta in a large saucepan of abundant boiling salted water. Drain it al dente and add to the vegetable sauce. Serve immediately, very warm, with a sprinkle of Parmesan cheese.