To Cook the Lobster Tails
Fill a large dutch oven with water and bring to a boil
Add thawed lobster tails and bring back to a boil
Reduce heat to medium and simmer about 6 minutes or until the internal temperature reaches 180 degrees
Remove the lobster tails, reserving the lobster water, and allow to cool
Using a sharp knife or kitchen shears, cut the lobster in half lengthwise
Remove the lobster meat, reserving the shells, and chop into small pieces
To Make the Lobster Broth
In a large dutch oven, over medium heat, melt 2 Tbsp butter
Add the shallot, carrot, celery, and garlic and sautee for about 3 minutes
Whisk in the tomato paste and cook another 3 minutes
Add the wine and the cognac to the pan and cook another 2-3 minutes
Add the lobster shells, 2 cups of the lobster water, seafood broth, thyme, bay leaf, and salt
Bring to a boil, then reduce heat to medium and simmer covered for 1 hour
Strain the broth through a fine sieve
To Make the Bisque
In a large dutch oven, over medium heat, melt 4 Tbsp butter
Whisk in the flour and cook 3-4 minutes until the mixture begins to brown and smell nutty
Whisk in the lobster broth and the heavy cream and bring to a simmer
To Serve
Divide the lobster meat between 6 soup bowls
Pour 1/6th of the lobster bisque over each bowl