Bring a large pot of salted water to a boil. Carefully add the lobsters, cover, and cook for about 10 minutes until they are bright red.

Once cooked, remove the lobsters and let them cool slightly. Extract the meat from the claws and tails, chop it, and set it aside.

In the same pot, melt the butter over medium heat. Add onions, carrots, celery, and garlic, cooking until they are softened and fragrant, about 5 minutes.

Stir in the tomato paste, thyme, and cayenne pepper. Cook for another 2 minutes.

Add the fish stock to the pot and bring the mixture to a simmer. Let it simmer for 10 minutes.

Use an immersion blender to puree the soup until smooth.

Return the pureed soup to the pot and stir in the heavy cream and chopped lobster meat.

Season with salt and pepper to taste. Serve hot, garnished with chopped chives.