Split 16 ounces lobster tails lengthwise with sharp kitchen shears. Remove meat and set aside. Add empty shells to stockpot or 4qt sauce pan. Cover with 15 ounces seafood stock and 4 cups water. Add 1 teaspoon Herbes de Provence and 1 teaspoon salt. Bring to a boil over high heat, then reduce heat as low as you can while still maintaining a simmer. Allow to simmer, uncovered, for about 15 minutes.
Add the lobster meat, cover with lid, and let simmer for 5 minutes. Remove when meat is bright red and white. If any part is still translucent, continue to simmer until cooked. Remove meat from pot and transfer to a cutting board. Cut into small pieces and refrigerate until ready to add to bisque.
BISQUE:
While the lobster stock is cooking, you can begin to make the bisque at the same time.
Heat 4 tablespoons butter over medium high heat in a large pot. Add 1 cup yellow onion, 1 cup carrots, and 1 cup celery. Stir to coat in butter and cook until soft, about 5-10 minutes, stirring occasionally to prevent burning.
When vegetables are just about done and begin to stick to the bottom of the pan, add 4 cloves garlic, stir to combine, and allow to cook for 1-2 minutes.
Add 2 tablespoons tomato paste, stir well to coat vegetables, and cook for 1-2 minutes.
Reduce heat to medium. Sprinkle 3 tablespoons all-purpose flour over mixture, stir well to combine, and cook while stirring frequently to prevent burning for an additional 2 minutes. The mixture should really start sticking to the bottom of the pan and turning brown. Do not allow it to burn.
Add 1 1/2 cups dry white wine to deglaze pan. Stir well with a flat bottom wooden spoon, scraping the bottom of the pan. Allow in wine to simmer for several minutes. The liquid will reduce and the mixture will become thick.
Set a fine mesh sieve or strainer over your pot and pour the lobster stock through the strainer into your pot. Discard shells. Stir broth into bisque base until well combined. Reduce heat to lowest setting to maintain a gentle simmer and allow to cook for about 30 minutes to allow flavors to develop. Stir occasionally during this time.
Remove bisque from heat. Use an immersion blender to purée the soup right in the pot. Alternatively, transfer to a blender to purée and then return bisque to pot.
Add 1 cup heavy cream and chopped cooked lobster pieces to bisque and stir well. Heat over medium-low heat until bisque is heated through. Season with salt and pepper, as desired. Serve hot with crusty bread on the side.
Notes
To reheat, I recommend heating gently in a saucepan over low heat. The microwave will work, but should be at a very low power in one-minute increments.