Lobster meat has a mild sweet flavor.  I think the tail is the best part of the lobster.  To ensure I have the best bisque I only use the tail and claws.

LOBSTER BISQUE

2 (4 oz.) lobster tails, 5 lobster claws, crackered, 3 tablespoons self-rising flour, 1 1/2 cup iced water, carrots, peeled and chopped, 1/2 cup celery, chopped, 1/4 cup red bell pepper, chopped, 4 garlic cloves, minced, 3 tablespoons tomato paste, 3/4 teaspoon seafood seasoning salt, 1/4 teaspoon white pepper, 1 teaspoon Worcestershire sauce, 1 bay leaf, 1/2 teaspoon dried thyme.

First things first.  Remove the lobster from the shell.  Get out a pot add the shells to the pot along with a bay leaf, 1 small red onion, 1 celery stalk, 1/2 teaspoon seafood seasoning salt, 1/2 teaspoon white pepper, add 3 cups of water. Bring to a rapid boil, reduce to a simmer, cover the pot a cook for 30 minutes. Remove to the heat, strain, and reserve the broth. Roughly chop one of the tails, cut the other tail into 4 pieces, set aside.  Make a white sauce. Get out a saucepan, add the butter, melt over medium heat; add the milk, flour, and butter stir with a whisk until blended and smooth, set aside.  Get out the dutch oven, add the iced water, claws, and crab boil simmer for 20 minutes. Remove the pot from the heat, set aside. Get out another pot, add the heavy whipping cream, evaporated milk, lobster stock, cognac, tomato paste, butter, and flour stir together until the flour dissolves simmer for 5 minutes.  Get out a skillet, add 1/2 tablespoon of butter flavored shortening, melt the shortening add the onions, carrots, celery,  bell pepper,  garlic, seafood seasoning salt, white pepper, Worcestershire sauce, bay leaf, and thyme saute until the onions are translucent. Add to the pot with the milk mixture, simmer for another 5 – 7 minutes. Add the chopped lobster tail and claws, cook for another 12 – 15 minutes. Serve with your favorite croutons or crackers.