For the Bisque:
3 lobsters, live female
3 tablespoons olive oil
1/2 cup brandy
1 cup lemongrass, sliced, dry ends discarded
2 cups sliced red onion
2 cups sliced fennel
3/4 cup minced ginger
2 tablespoons minced garlic
1/2 cup tomato paste
2 teaspoons Thai red curry paste
1/2 cup freshly squeezed lime juice
6 cups canned unsweetened coconut milk
2 dried bay leaves
7 sprigs fresh thyme
1/2 teaspoon crushed red pepper flakes
salt and freshly ground white pepper to taste

For the Garnish:
2 mangoes, peeled, pitted, and finely diced
2 tablespoons fresh basil, minced
1 tablespoon unseasoned rice wine vinegar

To prepare the Bisque:
Place a live lobster on a cutting board and, using a cleaver or sharp chef's knife, cut down through the middle of the lobster head to reveal the dark green egg sack (coral); carefully remove it and reserve. Remove and discard the remaining innards from the head. Use the cleaver or knife to separate the claws, claw joints, and tail from the body. Chop the claws and body into 2- to 3-inch pieces; leave the tail whole. Repeat for the remaining lobsters.

Heat 2 tablespoons of the olive oil in a large saucepan or stockpot and set over high heat until the oil is hot and shimmering. Add the lobster pieces and heads and cook until the shells are bright red, 8 to 10 minutes. Remove the lobster shells from the pan and transfer to a bowl. Pour the brandy into the pan and, using a wooden spoon, deglaze over medium heat for 1 to 2 minutes. Pour the contents of the pan into the bowl containing the lobster.

Heat the remaining 1 tablespoon of oil in the same pan over medium-high heat until it is hot and shimmering. Add the lemongrass, red onion, and fennel and cook until wilted, about 8 minutes. Add the ginger and garlic and cook for 3 minutes longer. Add the tomato paste and curry paste and cook for another 2 minutes. Add the lime juice, coconut milk, 6 cups of water, the bay leaves, thyme, and red pepper flakes. Return the lobster shells and brandy to the pan, stir well, and bring to a boil. Turn down the heat and simmer for about 4 minutes.

Remove the lobster tails from the soup and set aside to let cool. Then remove the tail meat from the shells, dice, and set aside.

Pass the lobster roe through a fine-mesh sieve and whisk it into the soup. Continue to simmer the soup, uncovered, for 1 hour. Strain the soup into a clean saucepan and adjust the seasoning with salt and pepper; keep warm over low heat, stirring occasionally.

To Prepare the Garnish:
Place the mango in a mixing bowl and add the diced lobster tail meat. Add the basil and vinegar and mix well.

To Serve:
Arrange the lobster and mango in the center of warm soup bowls and carefully pour the soup on top.

*Chef's Note:
This recipe calls for female lobsters because they contain coral, the name given to the unfertilized eggs or roe of the lobster. coral is so called because, when cooked, this caviar turns a lovely pink-red coral color.