In a large pot, bring 3 liters of water to a boil with sliced onions, sliced carrot, 1 sprig thyme, 2 bay leaves, parsley stalks, celery stalk, 30 cl dry white wine, salt, and pepper. Simmer for 5 minutes, then add the crab and cook for 20 minutes.
Let the crab cool, then peel and extract the flesh from the shell, legs, and claws. Break the chest in half, empty it, and reserve the coral.
Meanwhile, boil the Charlotte potatoes in salted water for 20 minutes. Drain, cool under cold water, and peel.
In a bowl, coarsely mash the potatoes with a fork. Add olive oil, chopped flat-leaf parsley, remaining white wine, crab coral, salt, and pepper. Mix well.
Arrange the potato mash in a neat disk on four plates using a spatula. Top with the crumbled crab meat.
Serve warm with thin lemon slices for a fresh zing.