Peel and finely dice the onions and garlic. Heat 2 tablespoons of oil in a saucepan, fry the onions and garlic. Add tomato paste and sauté briefly. Add tomatoes, chop with a spatula and let everything simmer at low heat for about 30 minutes. Melt the fat in a saucepan. Dust with flour and sauté while stirring. Gradually stir in stock and milk, let simmer for 5-8 minutes, stirring from time to time. Season to taste with salt and pepper
Clean, peel, wash and thinly slice the carrots. Wash, clean and slice the zucchini. Wash, clean and slice the beans. Drain artichokes in a sieve and cut in half. Cook the beans in boiling salted water for about 5 minutes. Heat 4 tablespoons of oil in a large frying pan. Sauté the carrots in it. Cook for approx. 5 minutes while turning
Drain the string beans, rinse with cold water and drain. Add zucchini to the carrots and fry for 2-3 minutes. Add cut beans and artichokes, season with salt and pepper. Wash the basil, dab dry. Pluck leaves and chop finely, except for something to garnish. Stir into the tomato sauce. Season tomato sauce with salt, pepper and sugar
Grease the fat pan of the oven. Spread some béchamel sauce on the bottom of the pan. Line with about 8 lasagne plates. Spread about half of the vegetables on top, sprinkle with 40 g Parmesan cheese. Pour about half of the béchamel and tomato sauce over it. Cover with another approx. 8 lasagne plates
Repeat the process with vegetables, 40 g cheese, béchamel and tomato sauce. Drain the mozzarella and cut into slices. Spread the mozzarella and 60 g Parmesan cheese on the casserole. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for about 30 minutes. Cut into pieces, garnish with basil and serve