Add the reserved shrimp shells to a saucepan with 4 cups of water. Bring to a boil, reduce the heat to low and simmer for 30 minutes. Remove from the heat and pour through a sieve, discard the shells. Measure the broth adding additional water to make 4 cups. Reserve.
For the Shrimp Bisque:
Heat the oil In a 4 quart Dutch oven or heavy-bottomed saucepan set over medium heat, add the chopped shallots and sauté until soft, do not brown them, 3-4 minutes. Add the garlic and cook for another minute.
Add the cayenne pepper and the shrimp. Cook until the shrimp turn pink, 3-4 minutes. Remove 6 of the shrimp and reserve for garnish. Add the brandy and cook for 1-2 minutes, add the sherry and cook for another 3 minutes. Working in batches, purée the mixture in a blender until smooth.
Melt the butter in the Dutch oven set over medium-low heat and whisk in the flour, cook for 1 minute then stir in the cream and milk, whisking until thick and smooth. Add the shrimp broth, puréed shrimp mixture, tomato paste, salt and pepper. Cook until hot while whisking continually. Do not let the bisque boil as the cream will curdle, adjust the heat as necessary.
To serve:
Ladle the soup into bowls, garnish with the reserved shrimp and chopped parsley. Drizzle a tablespoon of truffle oil on each serving.
Notes
Using frozen shrimp: Frozen, shelled shrimp can be used. Just thaw them overnight in the refrigerator.Broth substitute: Store-bought fish broth works if you’re not making the homemade shrimp stock.Temperature control: Keep the bisque below a simmer once the cream is added to prevent curdling.Safe blending: When blending hot bisque, fill the blender no more than halfway. Vent the lid by removing the center cap and cover it with a kitchen towel to allow steam to escape.Storing leftovers: Refrigerate leftover bisque and reheat gently over low heat.Fixing separation: If the bisque separates, use an immersion blender to bring it back together.