Classic French Lobster Bisque (Silky, Shell-Rich Soup)

Ingredients

• 2 cooked whole lobsters, about 1 1/4 lb (565 g) each, meat removed and shells reserved
• 4 tablespoons (55 g) unsalted butter
• 1 medium yellow onion, chopped
• 1 medium carrot, chopped
• 1 celery stalk, chopped
• 1 small shallot, chopped
• 3 cloves garlic, smashed
• 2 tablespoons tomato paste
• 3 tablespoons uncooked white rice
• 1/4 cup (60 ml) Cognac or brandy
• 1 cup (240 ml) dry white wine
• 4 cups (960 ml) seafood stock
• 3 sprigs fresh thyme
• 1 bay leaf
• 4 parsley stems
• 1 cup (240 ml) heavy cream
• 1/8 teaspoon cayenne pepper, or to taste
• 1 teaspoon fresh lemon juice
• Kosher salt
• black pepper
• 2 tablespoons chopped fresh chives