In a large saucepan, melt 4 tablespoons of butter over medium heat until frothy. Add 1 cup of minced shallots and sauté for about 4 minutes, or until they become translucent.

Sprinkle in 3 tablespoons of all-purpose flour, stirring continuously for 2 minutes to create a roux.

Gradually whisk in 2 cups of clam juice and 2 cups of low-sodium chicken stock, stirring to avoid lumps. Bring the mixture to a boil, then reduce the heat to low and simmer for 10 minutes.

Chop 1 pound of medium shrimp into ¼-inch pieces. Slowly pour in 1 cup of heavy cream and 1 cup of champagne, returning the bisque to a gentle simmer.

Remove the soup from heat and gradually add 2 cups of shredded Gruyère cheese, stirring continuously until melted.

Stir in the chopped shrimp and 2 tablespoons of chopped fresh chives, cooking for an additional 3 minutes until the shrimp turn opaque.

Ladle the warm bisque into bowls, garnishing with more Gruyère cheese and a sprinkle of chives. Serve immediately with crusty bread.