Place a large sharp knife into the head and split the lobster down the middle. Discard intestinal tract and sac behind head. Separate claws and tail from body and crack claws. Cut body and tail into 4 or 5 pieces.
Tie the parsley, thyme and bay leaf together to make a bouquet garni.
Melt the butter in deep skillet over medium-high heat. Add lobster parts; cook, covered, turning once, until bright red, 6 - 7 minutes. Remove skillet from heat and pour lobster-infused butter into a bowl and set aside. Pour brandy over lobster; ignite with a match. When flame subsides, transfer lobster to a plate and remove the meat.
In a stock pot, heat the fish stock, bouquet garni and lobster shells over medium heat and bring to a simmer for 20 minutes. Remove from heat and pour stock through a fine-mesh strainer; reserve.
Meanwhile, add the lobster-infused butter back to the large skillet over medium-high heat. Add the carrots, celery, onion and rice and cook, stirring occasionally, until the onion is soft, about 7 minutes. Stir in the tomato paste and cook until the tomato has darkened in color and it aroma has softened, 5 to 7 minutes.
Add the wine, bring to a boil, and boil for 4 minutes. Add the reserved stock, reduce the heat to low, and simmer gently until the rice is fully cooked, about 15 minutes.
Meanwhile, dice half of the reserved lobster meat and reserve for a garnish. Stir the remaining lobster meat into the stock and remove from the heat.
Puree with an immersion blender, or, transfer the soup to a blender, and working in batches, blend, gradually increasing the speed, until the mixture is very smooth and silky (always take care when blending hot liquids). Strain the soup though a fine-mesh strainer, pressing on the solids with the back of a ladle. Discard any solids that do not pass through.
Gently reheat the bisque and whisk in the cream, adding more fish stock if bisque is too thick.
Taste and add salt and pepper, to taste.
Divide the bisque among bowls and garnish with the reserved diced lobster meat. Serve immediately.