Clean and crack the crabs, then remove the meat from the shells. Place the crabmeat in a small bowl, cover and refrigerate. Use kitchen shears to cut the crab shells into small pieces. Reserve the shells.
In a 6- to 8-quart saucepan, over low heat, melt the butter and swirl to coat the pan. Add the onion, carrots, and celery and sauté, stirring frequently, until the vegetables are softened, about 12 minutes. Mix in the flour. Add the garlic and crab shells and stir until the crab shells turn bright red, about 8 minutes. Stir in the tomato paste and wine, then stir to combine. Continue cooking for 5 minutes. Add the water and the clam juice and stir to blend the ingredients. Bring the mixture to a simmer and cook, stirring occasionally, for 20 minutes, to allow the flavors to meld.
Strain the mixture through a fine mesh sieve into a clean saucepan, reserving the solids, including the shells. Using a blender, process the solids until finely ground. (This step extracts extra flavor from the shells.) Pour into a fine-mesh sieve lined with cheesecloth and placed over a bowl. Pour the brandy and cream over the solids in the sieve. Using the back of a spoon, press down on the solids to extract as much liquid as possible. Add the liquids to the pot holding the strained crab stock.
Add the cayenne, Tabasco sauce and salt to the pot and bring to a simmer over medium-high heat. Cook until heated through, about 10 minutes. Add the reserved crabmeat. Season to taste with salt and additional cayenne, if desired. Ladle the soup into warmed soup bowls. Serve immediately.