In a large stockpot, melt butter over medium-high heat. Add shallots and cook until softened, 4-5 minutes. Sprinkle flour over shallots and cook, stirring constantly, for 2 minutes.

Whisk in clam juice and chicken broth. Bring to a boil; boil for 10 minutes until slightly thickened.

Stir in Half & Half, white pepper, Worcestershire, and Champagne. Bring to a simmer.

Sprinkle in half of the cheese, stir until melted, then add the rest of the cheese and stir until melted.

Bring back to a simmer, then add the shrimp and cook for 3-5 minutes, until all the shrimp are opaque.

Ladle into bowls and garnish with chives. Serve with crusty bread.