How to Make It
In a small saucepan, cover the shrimp shells with the water and bring to a boil. Simmer for 20 minutes, then strain the shrimp stock into a bowl.
Meanwhile, in a large skillet, heat the olive oil. Add the shrimp, garlic, onion and cayenne and cook over high heat until the shrimp begin to turn pink, about 3 minutes. Add the brandy and boil until reduced by half, about 2 minutes. Add the chopped basil and the sherry and simmer until the shrimp are just cooked through, about 2 minutes. Transfer the shrimp to a food processor, add the shrimp stock and puree until smooth.
In a medium saucepan, melt the butter over moderate heat. Whisk in the flour and cook, whisking, until smooth, about 1 minute. Slowly whisk in the half-and-half and cook, whisking, until the roux is very thick, about 2 minutes.
In a soup pot, combine the fish stock with the tomato paste and the shrimp puree and bring to a simmer over high heat. Slowly whisk in the roux and the heavy cream. Reduce the heat to moderately low and simmer until thick and creamy, about 20 minutes. Add the lemon juice and season with salt and pepper. Ladle the bisque into bowls, garnish with the sliced basil and serve.