Bring a large pot of salted water to a rolling boil. Add live lobsters and cook 8–10 minutes until shells are bright red and meat is cooked through. Transfer lobsters to an ice bath to stop cooking. When cool enough to handle, remove tails and claws. Crack shells and reserve all shells and bodies for stock. Remove tail and claw meat; refrigerate about 1 cup for garnish and set aside. Roughly chop any large pieces of meat for later.

Sauté shells & vegetables

In a large heavy-bottomed pot or Dutch oven, melt 3 tbs butter over medium heat. Add the chopped onion, celery, carrot and smashed garlic. Sauté, stirring occasionally, until vegetables soften and begin to brown, about 8–10 minutes. Add the reserved lobster shells and cook, stirring occasionally, 5–7 minutes to develop color.

Deglaze & simmer

Stir in 2 tbs tomato paste and cook 2 minutes. Pour in the white wine to deglaze, scraping up browned bits from the bottom. Add 8 cups cold water, bay leaves, peppercorns, thyme, and 1 tsp kosher salt. Bring to a gentle simmer, then reduce heat to low and simmer uncovered for 40–50 minutes, partially covered.

Strain stock

Strain the stock through a fine-mesh sieve into a clean pot or large bowl, pressing on solids to extract liquid. Discard solids. Skim excess fat from the surface if desired. Taste and adjust seasoning lightly; set warm.

Bisque Base & Finish

Make roux and build flavor

In a clean heavy pot, melt 4 tbs butter over medium heat. Add the finely chopped shallots and cook until translucent, 3–4 minutes. Stir in 3 tbs flour and cook, stirring constantly, 2–3 minutes to make a light blond roux. Add 1 tbs tomato paste and stir 1 minute.

Add stock and simmer

Slowly whisk in about 4 cups of the warm lobster stock until smooth, then add remaining stock (about 4 more cups). Bring to a gentle simmer and cook 15 minutes, whisking occasionally, to thicken and meld flavors.

Purée and strain

Using an immersion blender (or working in batches in a countertop blender), purée the soup until very smooth. For an ultra-silky bisque, pass the puréed soup through a fine-mesh sieve or chinois, pressing with the back of a ladle to extract the smooth puree. Return the strained bisque to the pot and keep over low heat.

Finish with cream & seasonings

Stir in the heavy cream and whole milk, then add 3 tbs dry sherry (or brandy). Warm gently—do not boil—until the soup is heated through and slightly thickened, about 5–7 minutes. Season with 1 tsp salt, 1 tsp freshly ground black pepper, 1 tsp paprika, 1 tsp cayenne (adjust to taste), and 1 tbs lemon juice. Taste and adjust seasoning and acidity. Keep warm.

Lobster Meat Garnish

Warm lobster meat

In a small skillet, melt 2 tbs butter over medium-low heat. Add the reserved chopped lobster meat and gently warm for 1–2 minutes until just heated through. Season with 1/4 tsp salt and 1/4 tsp freshly ground black pepper. Do not overcook to avoid toughness.

Assemble & serve

Ladle bisque into warmed bowls. Divide the warmed lobster meat evenly among bowls (about 2–3 tbs per serving). Garnish with 2 tbs chopped fresh chives sprinkled across the bowls. Optionally drizzle a teaspoon of cream or a few drops of sherry on top. Serve immediately with crusty bread or croutons.