Shorten the ends of the asparagus and cut the stalks into pieces about 4 cm long. Wash the celery, pull off the coarsest fibers from bottom to top and cut the stick into fine slices. Wash the zucchini and cut into sticks. Peel and chop the carrots and potatoes. Scald the tomatoes, rinse and peel them, dice the pulp. Peel onion and garlic and chop finely.
Heat the clarified butter in a large saucepan and fry the onions and garlic until translucent. Add the carrots and potatoes and fry briefly. Pour in the broth, bring to the boil and cover the soup and simmer for 10 minutes. Add the rest of the vegetables, season and cook, covered, for about 8 minutes, until the vegetables are cooked but still firm to the bite.
In the meantime, wash the parsley, shake dry and chop without the coarse stalks. Season the soup to taste and serve sprinkled with the parsley.