Cook the Lobsters: In a large pot, bring water to a boil. Add the live lobsters and cook for about 10 minutes until they turn red. Remove from water and let cool.
Remove the Meat: Twist off the lobster tails and claws. Remove the meat and chop it into small pieces. Set aside.
Make the Base: In a large pot, melt the butter over medium heat. Add the onion, carrots, celery, and garlic. Cook until vegetables are soft, about 5 minutes.
Add Flavor: Stir in the tomato paste and cook for another 2 minutes. Add the brandy and cook until it reduces by half.
Add Broth: Pour in the fish or vegetable broth and bring to a simmer. Cook for 20 minutes.
Blend: Use an immersion blender to puree the soup until smooth. Strain through a fine mesh sieve to remove any solids.
Finish: Return the soup to the pot and stir in the heavy cream. Add the chopped lobster meat and season with salt and pepper. Cook for another 5-10 minutes.
Serve: Ladle the lobster bisque into bowls and garnish with chopped chives. Enjoy!
