Fill a medium pot with 5 cups of water and bring to a boil.
Meanwhile, wash the lobster tail and cut the top shell up to the fin with scissors. This way, you will have easy access to the meat once it is cooked.
Add lobster tail in boiling water, reduce heat and simmer for 4 minutes or until shell turns slightly red.
Turn off heat. Remove lobster from water and leave lobster broth in pot. Pry open the shell with 2 forks and cut the meat at the fin with scissors.
Add the shells back in the pot, set heat to high and bring to a boil. Then lower heat to low and simmer for at least 30 minutes to an hour to extract as much flavor from the shell. The broth will be reduced to about 4 cups.
Turn off heat. Leave the shells in the broth until ready to use. Set aside.
Make Lobster Bisque
In a large pot, heat butter over medium low heat.
Saute the aromatics. Add the onion, garlic, carrots and celery. Cook until they start to release their juices into the pan about 3 to 5 minutes.
Remove from pot and transfer to a bowl.
Make the roux. On the same pot, melt butter over medium-low heat then add ½ of the flour stirring constantly until blended. Add the bacon grease and the remaining flour stirring constantly until golden (not brown) about 3 to 4 minutes.
Add back the sauteed aromatics and blend well with the roux or flour mixture.
Stir in the tomato paste, thyme, tarragon and bay leaves. Continue to cook for another 2 minutes.
Add white wine and deglaze the pan. Cook until liquid is reduced to half.
Stir-in chicken powder bouillon then pour 4 cups of the reserved lobster broth. Note: If you don’t have enough broth, I recommend any seafood stock preferably Bar Harbor's clam juice otherwise use vegetable or chicken stock.
Adjust heat to high and bring to a boil. Once boiling, lower heat to medium-low, cover pot and simmer for ½ hour.
Carefully puree mixture with an immersion blender otherwise use a regular blender and puree in batches. Check notes below.
Slowly pour heavy cream while stirring constantly until well blended. This soup is creamy but not super thick. If you like it thicker, add more cream.
Stir-in lobster meat and continue cooking for ½ a minute.
Turn off Heat. Serve while hot and garnish with cayenne pepper and thyme, if desired.
Cold lobster bisque (chilled) is delicious as well.
If using regular blender to puree soup - Fill the blender jar ½ full, remove the center piece on lid so steam can escape and put the lid and blend on low. Most high powered blender can blend hot soup otherwise let the mixture cool before blending then reheat again before pouring the heavy cream.
I suggest to use fresh thyme and fresh tarragon. You can substitute with ½ teaspoon dried thyme and ¼ teaspoon dried tarragon. Dried herbs are more potent than fresh ones.
You can quickly saute lobster meat in melted unsalted butter and a pinch of garlic powder before adding to the soup.
Serve lobster bisque with bread and your favorite wine.