Bring a large pot of salted water to a boil. Drop live lobsters into boiling water for 6–8 minutes until shells turn bright red (par-cook). Remove and transfer to an ice bath to stop cooking. Reserve cooking liquid if desired. Remove meat from tails and claws and set aside refrigerated for finishing. Reserve shells (cracked) for stock.

Sear shells and vegetables

In a large heavy pot, melt 2 tbs butter over medium-high heat. Add cracked lobster shells and sauté 4–5 minutes until they begin to brown and become fragrant. Add chopped onion, carrot and celery and continue to sauté 5–6 minutes until vegetables soften. Stir in tomato paste and smashed garlic and cook 2 minutes to remove raw flavor and deepen color.

Deglaze and simmer

Pour in the sherry and white wine, scraping up browned bits from the bottom. Let alcohol reduce by half (about 2–3 minutes). Add water, bay leaf, peppercorns, thyme and 1 tsp salt. Bring to a simmer, then reduce heat to low and simmer gently, uncovered, for 35–40 minutes to extract flavor from shells and vegetables.

Strain stock

Strain the stock through a fine-mesh sieve into a clean pot or bowl, pressing on solids to extract as much liquid as possible. Discard solids. If you prefer an ultra-smooth bisque, return strained stock to the pot and skim fat, then optionally pass through a chinois or fine chinois/cheesecloth.

Meat & finish

Reduce stock and blend (optional for thicker bisque)

Return 4 cups of the strained lobster stock to the pot and simmer until reduced to about 3 cups (10–15 minutes) for a more concentrated flavor. If you want a silkier, thicker texture, reserve 1/2 cup of the reserved lobster meat and pulse it in a blender with 1/2 cup stock until smooth, then return to the pot.

Enrich with cream

Lower heat to medium-low. Whisk in the heavy cream and milk, stirring to combine. Simmer gently (do not boil) for 5–7 minutes until warmed through and slightly thickened.

Finish and adjust seasoning

Stir in the remaining lobster meat chunks, 1 tbs butter, and 1 tbs fresh lemon juice. Heat just until the meat is warmed through (1–2 minutes). Taste and adjust seasoning with salt and freshly ground black pepper as needed. Keep warm on very low heat while you make croutons.

Lemon croutons & garnish

Make lemon croutons

Preheat oven to 375°F (190°C). Toss bread cubes with olive oil, melted butter, lemon zest and sea salt on a rimmed baking sheet. Spread in a single layer and bake 8–10 minutes, tossing once, until golden and crisp. Remove and cool slightly.

Serve

Ladle bisque into warmed bowls. Top each bowl with a few lemon croutons and a sprinkle of finely sliced chives if using. Optionally drizzle a teaspoon of sherry or a splash of cream over each bowl. Serve immediately.