Bring 4 cups of water to a boil in a large pot. Add the lobsters and cook for about 10-12 minutes until they turn bright red. Remove the lobsters from the pot and let them cool. Reserve the cooking water.
Once cool, extract the meat from the lobsters, chop it into bite-sized pieces, and set aside. Retain the shells for added flavor.
In the same pot, heat olive oil over medium heat. Add chopped onion, carrot, celery, and garlic. Sauté for about 5-7 minutes until the vegetables are softened.
Add the reserved lobster shells to the pot and cook for an additional 5 minutes to build flavor.
Pour in the brandy and allow it to cook off for 2-3 minutes. Then stir in the tomato paste.
Add the reserved lobster cooking water and seafood stock to the pot. Bring to a simmer and cook for 30 minutes, allowing the flavors to meld.
After simmering, use a strainer to separate the liquid from the solids. Discard the shells and solids, then return the liquid to the pot.
Stir in the heavy cream, paprika, and the reserved lobster meat. Season with salt and pepper to taste. Heat gently for another 5 minutes to warm through.
Ladle the bisque into bowls and garnish with fresh chives or parsley. Serve hot.