Bring a large pot of water and boil it over high heat, and add 2 tablespoons kosher salt. Drop in the lobsters, and cook until they turn bright red, 8-10 minutes.
Once you cook the lobsters, remove them from the boiling water and reserve the water for later use. Let the lobsters be cool enough to handle them without burning yourself. Separate the Meat from the Shells. Carefully remove all the meat from the shells, and set aside.
In a large Dutch oven or heavy pot over medium-high heat, add 2 tablespoons olive oil and the shells of the lobsters. Sauté until they’re lightly browned, about 8 minutes.
Add 2 cloves garlic (minced), 2 sprigs of fresh thyme, 2 sprigs of fresh tarragon, 1 chopped carrot, 2 ribs of celery (chopped), and 1 medium onion (chopped). Sauté for 5 minutes more.
Add the fish stock or clam broth to the pot and bring it to a boil. Reduce the heat and simmer for 30 minutes. Strain the stock through a fine-mesh strainer, discard the solids, and return the stock to the pot.
In a medium saucepan over medium heat, add 2 tablespoons tomato paste and cook for 1 minute. Add 1 cup medium sherry to the pan and simmer until it’s reduced by half.
Add the sherry mixture to the pot with the stock, and return it to a boil. Add ½ cup long-grain white rice, reduce the heat to low, and simmer for 20 minutes.
Stir in 1 cup heavy cream, season with cayenne pepper, and cook for 2 minutes more. Add the lobster meat to the pot and cook until it’s heated through about 2 minutes. Serve hot.