In a large stockpot, bring 4 cups of water to a boil. Add the live lobsters, cover, and cook for about 8-10 minutes until they are bright red. Remove lobsters and let them cool.

Once cooled, remove the meat from the lobster tails and claws. Chop the meat into bite-sized pieces and set aside. Reserve the shells for later.

In the same stockpot, heat 2 tablespoons of olive oil over medium heat. Add the chopped onion, carrots, and celery, and sauté until soft, about 5-7 minutes.

Add minced garlic, tomato paste, thyme, and bay leaf. Cook for another 2 minutes, stirring frequently.

Add the reserved lobster shells to the pot. Pour in 4 cups of water and bring to a simmer. Let it cook for about 30 minutes to meld the flavors.

After 30 minutes, remove the pot from heat. Using a strainer or fine mesh sieve, strain the broth into a large bowl, discarding the shells and vegetables.

Return the broth to the pot, and stir in the heavy cream and brandy (if using). Heat on low until warmed through.

Blend the soup until smooth if desired, using an immersion blender or regular blender. Return to heat, add lobster meat, and season with salt and pepper to taste.

Serve hot, garnished with fresh parsley if desired.