Wash the aubergine, remove the stem and cut into cubes about 1 cm. Sprinkle with salt and leave covered for about 1/2 hour.
In the meantime, cut the fresh tomatoes crosswise, scald them with hot water, peel them, remove the core and chop the pulp.
Finely chop the onion and garlic and sauté in olive oil until translucent. Pat dry the aubergine cubes, add and fry vigorously. Add the chopped tomatoes and fill up with the vegetable stock. Season with freshly ground pepper, salt and a pinch of sugar. Let everything simmer for about 20 minutes. Season the soup with about half of the sweet cream.
Pluck the basil leaves from the stalks, keep a few leaves for decoration, roughly chop the rest and stir into the soup at the end of the cooking time.
Arrange the aubergine soup in four soup plates, garnish each with 1 tablespoon of sweet cream and basil leaves.