Prepare lobster by cutting in half lengthwise through the head and body first. Remove tail halves, and claw and knuckle sections.
These are the sections with the meat for the bisque. Cut the body into 2-inch pieces.
Heat oil over medium high heat in a 4-quart stock pot and add the chopped onions, shallots, garlic, celery, carrots and all of the lobster.
Cook on medium to medium high heat, stirring continually for 10 to 12 minutes.
Remove just the lobster pieces which contain meat and let cool for 10 minutes.
Deglaze the pan with the sherry.
Add the peppercorns, cayenne, parsley, bay leaves, thyme and tomato puree. Cook stirring for another 5 minutes.
Place the water and heavy cream into pot and bring to a boil.
Remove lobster meat from cooled lobster and reserve for the final presentation.
Add the remaining shells to the creamy stock. Let simmer and reduce by 1/4.
In a separate 3 - 4 quqrt pot, melt butter on medium heat. Stir in flour with a wire whisk to make a roux. Lower heat and slowly cook the flour and butter for about 5 minutes. The roux should be blond in color and have a buttery aroma.
When the creamy stock is reduced, strain into the pot with the roux, and whip with a wire whisk. Discard the shell and vegetable mixture.
Chop the lobster meat into 1/2-inch pieces and stir into bisque. Salt and pepper to taste.
Portion bisque into your favorite cup or bowl and garnish with chopped chives.
