Shrimp Bisque

Melt 1/4 cup butter in a large stockpot over medium. Add tomatoes, onion, carrot, and celery; cook, covered, stirring occasionally, until vegetables are soft, about 7 minutes. Increase heat to high, and add shrimp shells and rice; cook, stirring often, until shells turn deep red, 2 to 3 minutes. Stir in tomato paste; cook, stirring often, until browned, about 2 minutes. Remove from heat, and stir in brandy. Return to heat over high, and cook, stirring occasionally, until liquid has almost evaporated, 2 to 3 minutes.

Tie together parsley, thyme, and bay leaf using kitchen twine to make a bouquet. Add herb bouquet, 9 cups water, and 2 teaspoons salt to mixture in pot; bring to a boil over high. Reduce heat to medium-low; cover and simmer 30 minutes. Remove from heat. Uncover and let cool briefly, about 10 minutes. 

Remove and discard herb bouquet from soup mixture. Working in 2 batches, pour soup mixture into a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until completely smooth, about 1 minute. Pour through a fine wire-mesh strainer into a 6-quart saucepan; discard solids.  

Bring bisque in saucepan to a low simmer over medium. Whisk in cream, lemon juice, black pepper, cayenne pepper, remaining 1/4 cup butter, and remaining 1 1/2 teaspoons salt until smooth and well combined. Adjust seasoning with additional salt, lemon juice, black pepper, and cayenne pepper to taste. 

Divide bisque evenly among bowls. Garnish with crème fraîche, chives, and paprika, cayenne pepper, or Old Bay seasoning, as desired.