Bisque is currently used as a general term for a thick puréed or otherwise creamy soup that's usually made with cream or crème fraîche. Traditionally, "bisque" refers to a complex shellfish soup that is classically made with lobster, crab or crawfish.

To make a classic bisque, shellfish is cooked in a mirepoix, flamed with cognac and reduced with white wine and stock. The shellfish is allowed to cool, then shelled and the flesh is chopped to use as a garnish for the soup.

The shells are pounded, then mixed with cooked rice and the flavored broth to form a purée that is strained, thinned with more stock, boiled and then enriched with butter and cream and garnished with the reserved shellfish.

Recipe: Watercress Bisque (Washington Post)
Recipe: Shrimp Bisque (Cookthink)