Heat the vegetable oil very hot in a large saucepan. Remove the meat from the claws and reserve. Add the shells to the hot oil and and stir-fry until the edges begin to turn dark brown. Pour off the excess oil.
Remove the pot from the fire and very carefully add the brandy. (You can flame it if you like, but be careful.) Return the pot to the fire and cook, tossing around, until the brandy is evaporated.
Add the tomatoes, onions, carrots, celery and garlic and continue to cook over high heat, stirring often. When vegetables are tender, add the crushed red pepper and white wine. Let the wine come to a boil, then lower the heat.
Add two quarts of cold water, bay leaves, tarragon, salt and pepper and return to a simmer. Hold at a simmer for one hour.
Add 1/2 cup of the stock from the pot to the rice, and puree the rice in a food processor or blender. Add this to the stock and continue to simmer for another 30 minutes.
Strain the soup through a colander. Puree the solids in a food processor with a little stock, and strain this once again through a coarse sieve into the soup.
Stir in the whipping cream and return the soup to a simmer. Adjust seasonings with salt, pepper, and cayenne. I think this should have a noticeable pepper glow in the flavor.
Place the reserved meat from two claws onto a soup plate. Ladle the soup over the claw meat.