Heat the salted water in a saucepan on the highest stove setting, add the pasta and swell for 8-10 min on 0.
In the meantime, rinse and clean the melanzani and cut them into slices about 1/2 cm thick. Place in a colander and sprinkle with salt, turn to the other side and rest for 30 min.
In the meantime, peel and finely dice the onion. Clean, rinse and chop the carrots and celeriac.
Drain and chop the tomatoes, removing the stalks.
Gently cook the onion, carrot and celery cubes in 3 tablespoons of olive oil on speed 2 1/2 or automatic heat for about 5 minutes. Add the finely chopped basil leaves and season with salt and pepper.
Preheat the oven to 200 °C (fan 180 °C, gas mark 3-4). Drain the pasta, drain well, mix with the vegetables and shape into an ovenproof gratin dish.
Dry the slices of melanzana well. Heat the remaining olive oil in a frying pan. Sauté the slices of melanzana in it on both sides and spread evenly on the casserole. Pour the liquid cheese cream over it.
Place the casserole in the preheated oven, 2nd rack from the bottom, and bake for about 30 minutes.
During frying, slices of melanzanera soak up like a sponge. To avoid this, sprinkle them with salt on both sides. This removes water from the flesh and causes the cells to constrict.
When you free melanzane from the skin