Trim the French beans, eliminate any filament and cut into small bits. Trim, peel, wash and cut the carrots into rounds. In a saucepan of boiling salted water blanch the carrots and the French beans for about 3 minutes.Then drain them and set aside. Peel the onion and slice it finely; peel the garlic, wash the parsley and mince them together. Trim, wash and cut the aubergine into small cubes, then salt them and drain well for about 20 minutes to allow them to give out their own water.In a pan with a drop of oil fry the onion, the garlic and part of the chopped parsley until soft. Add the drained aubergine cubes, the carrots and the French beans; fry lightly for another 3 minutes, constantly stirring with a wooden spoon.Add the tomatoes a pinch of salt and carry on cooking for another 20 minutes over a medium fire. Before removing from the heat, add the remaining chopped parsley and garlic. In the meanwhile, cook the conchiglioni in a large saucepan of abundant boiling salted water.Drain them al dente and season with the prepared sauce, mix well to make the sauce cling to the pasta. Serve immediately very warm with the grated parmesan cheese.