The basis for the crab soup is necessarily home-made vegetable broth! To do this, clean and wash the vegetables. Cut the leek and celery into fine rings, the carrots and parsley root into small cubes. Cut the fennel in half lengthwise, remove the stalk and cut the rest into thin strips.
Peel the onion and shallot and cut into thin rings. Rinse the parsley and thyme and place in a large pot with the unpeeled garlic, the vegetables and the ingredients thyme to cloves (but without salt!). Add water and white wine and bring to a boil over high heat. Reduce heat, close pot and simmer gently for about 45 minutes.
Skim off foam if necessary. Season to taste with sea salt. Fill a large bowl with plenty of ice cubes and place a large enough second bowl inside. Strain the broth through a fine-mesh sieve, preferably lined with a muslin cloth (baby diaper). The broth must be cooled down in a flash.
Vegetable broth that is not needed can be frozen very well. In the meantime, the crabs are poached (keep the shells), for example, during the day show the night before.
Place the shells in a saucepan, bring to a boil with just over a quart of vegetable broth. Reduce heat. If there are leftovers of low-fat fish (heads, bones, fins), they go in any case, then a little more broth is needed. Simmer gently in the closed pot for about 30 minutes.
Then also drain through a fine mesh strainer lined with gauze into a second pot. Add the cream and heat (no longer boiling!). Finally, season with Tabasco, lemon juice, sea salt and cognac. Divide the crabmeat evenly (fairly!) among four soup bowls, pour over the soup and sprinkle with the blanched, dried and finely chopped chervil (alternatively, chives cut into fine rolls and chopped dill tips also fit very well).