Fill a large pot with water and bring it to a boil. Add the live lobsters and cook for about 8-10 minutes until they turn bright red. Remove the lobsters from the pot and let them cool. Once cooled, remove the meat from the shells and set aside. Reserve the lobster shells for later.

In a large soup pot, melt the butter over medium heat. Add the chopped onion, carrot, celery, and garlic. Cook until the vegetables become soft and translucent.

Add the tomato paste to the pot and cook for an additional 2-3 minutes, stirring constantly. This will help develop the flavours.

Pour in the brandy or cognac and let it simmer for a minute to cook off the alcohol.

Add the lobster shells to the pot and stir to coat them with the mixture. This will infuse the soup with a rich lobster flavour.

Pour in the fish stock or seafood broth and bring the mixture to a boil. Reduce the heat and let it simmer uncovered for about 30-40 minutes, allowing the flavours to meld together and the soup to reduce slightly.

Using a blender or immersion blender, carefully puree the soup until smooth. Strain the soup through a fine mesh sieve to remove any solids and achieve a velvety texture.

Return the soup to the pot and stir in the heavy cream and paprika. Season with salt and pepper to taste. Gently reheat the soup over low heat, being careful not to boil it.

Once heated through, add the cooked lobster meat to the soup and simmer for a few more minutes until the lobster is warmed.

Ladle the lobster bisque into bowls, garnish with chopped fresh chives or parsley, and serve hot.

This classic lobster bisque is a luxurious and indulgent dish. It pairs well with crusty bread or oyster crackers for a complete meal. Enjoy the rich flavours and velvety texture of this exquisite soup, reminiscent of Julia Child's culinary expertise.