Start the Base: Melt butter in a large saucepan or Dutch oven over medium-low heat. Add the finely chopped green onion and celery, sautéing until they are soft and translucent to create the aromatic foundation of the bisque.
Incorporate Flour: Gradually stir in the flour, blending it thoroughly with the butter and vegetables. Stir constantly for about two minutes to prevent lumps and ensure the bisque thickens smoothly.
Add Milk: Warm the milk in a separate saucepan, then slowly pour it into the flour mixture while stirring continuously. Continue cooking until the mixture thickens to a smooth, creamy consistency.
Flavor the Base: Add the black pepper and tomato paste, followed by the heavy cream. Stir well to blend the flavors together.
Blend for Smoothness: For a silkier texture, use a blender or immersion blender to puree the mixture. This step is optional but enhances the smoothness of the bisque.
Add Seafood: Return the blended mixture to the saucepan, add the crab meat and shrimp, and pour in the sherry wine. Stir gently, then bring the bisque to a low simmer, allowing the seafood flavors to infuse without boiling.
