Step 1

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.

Step 2

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.

Step 3

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.