Preparing the Lobsters: Cook the lobsters by boiling or steaming, then remove the meat from the shells. Set the meat aside and reserve the shells for the broth.
Making the Broth: In a large pot, add the lobster shells and fish or seafood broth. Bring to a simmer and let cook for 30 minutes to infuse the broth with lobster flavor.
Straining the Broth: After simmering, strain the broth to remove and discard the lobster shells, leaving a clear, flavorful broth.
Blending the Lobster Meat: Take half of the cooked lobster meat and blend it with a portion of the broth until smooth. This will help thicken the bisque and add texture.
Combining: Return the blended lobster mixture to the pot with the remaining broth. Bring the mixture to a gentle simmer.
Adding Cream: Stir in the heavy cream, and if using, add salt and black pepper to taste. Warm the bisque through but avoid boiling it after adding the cream to prevent curdling.
Finishing Touches: Chop the remaining lobster meat into bite-sized pieces and add them to the bisque just before serving, warming through for a few minutes.
Serving: Ladle the creamy lobster bisque into bowls, ensuring there are pieces of lobster meat in each serving.