How to Make It
In a large saucepan, melt the butter in the oil. Add the shrimp and cook over moderate heat, stirring, until light golden and just white throughout, about 2 minutes. Transfer 8 of the shrimp to a plate to cool; finely chop and reserve them for adding to the finished bisque.
Add the reserved shrimp shells, the onion and garlic to the remaining shrimp in the saucepan. Cook over moderate heat, stirring occasionally, until the onion is softened, about 3 minutes. Add the tomato paste and cook, stirring, until lightly caramelized, about 2 minutes. Stir in the wine and cook until almost evaporated, about 1 minute. Stir in 6 cups of water and bring to a simmer. Cook over low heat for 25 minutes.
Working in 2 batches, puree the soup in a blender. Strain through a fine sieve set over a small saucepan, pressing on the solids. Bring the soup to a simmer and stir in the cream. Add the reserved chopped shrimp and season with salt and pepper. Ladle the bisque into bowls and garnish with chopped tarragon.