Heat oven to 400ºF (200ºC). Add the shells, onion, carrots and celery to a baking sheet and roast until browned, about 30 minutes.

Add to a large stockpot with the tomato paste, 12 cups of water, the garlic and peppercorns. Bring to a boil then reduce heat to medium-low and simmer for 1 hour.

Strain broth through a fine-mesh sieve and discard the solids. Season with salt to taste. Refrigerate broth in an airtight container for up to 1 week or freeze for up to 6 months.

Heat a large heavy pot over medium-high heat then add the oil and heat through. Add the onion, celery, and carrot (a mirepoix) and sauté until the onion becomes translucent and soft, about 10 minutes.

Add the garlic, thyme, tarragon, bay leaves, peppercorns, brandy, stirring, until almost all liquid is evaporated, about an additional 5 to 8 minutes.

Add the tomato paste and stir to combine then add the fish stock and 2 cups of water. Bring the mixture to a boil over medium heat then reduce heat to medium-low and simmer, uncovered, stirring occasionally until the mixture has reduced by about a third, about 30 minutes.

Remove the pot from the heat and pour the mixture through a fine mesh sieve into a large saucepan, pressing on the solids to extract as much liquid as possible. Discard the leftover solids.

Return the bisque to the pot over medium-low heat. Add rice and cook until the rice is extremely soft, about 30 minutes.

Add mixture to blender and blend until smooth. Strain through a fine-mesh sieve then return to pot.

Whisk in the cream and season with salt and pepper, to taste. Add ½ pound of the lobster meat and stir to combine, reserving some for garnishing the soup.

Divide among warmed soup bowls and top with the remaining lobster and finish with a bit of the brandy (optional).