Bring a large pot of salted water to a boil. Add the lobsters and cook for about 8-10 minutes until they turn bright red. Remove the lobsters, and let them cool. Reserve the lobster water for later use.
Once the lobsters are cool enough to handle, remove the meat from the claws and tails. Chop the lobster meat into bite-sized pieces and set aside. Reserve the shells.
In a large pot, melt the butter over medium heat. Add the chopped onion, carrot, and celery. Cook until the vegetables are softened, about 5-7 minutes.
Stir in the minced garlic and cook for an additional minute. Then, add the tomato paste, dried thyme, bay leaf, and cayenne pepper, and cook for another 2-3 minutes.
Add the lobster shells back into the pot, pour in the fish stock (or reserved lobster water), and bring to a boil. Reduce the heat and let it simmer for about 30 minutes.
After 30 minutes, remove the pot from heat. Carefully remove the shells and bay leaf. Use a blender or an immersion blender to puree the soup until smooth. Return to heat.
Stir in the heavy cream and brandy (if using). Heat through, but do not boil. Taste and season with salt and pepper as desired.
Finally, add the reserved lobster meat to the bisque. Allow it to warm through for a few minutes.
Serve the lobster bisque hot in bowls, garnished with chopped fresh chives or parsley.