1. Have the lobster split and cleaned at the market. Crack the claws and cut the body and tail into four or five pieces.
2. Melt two tablespoons of the butter and saute the carrot and onion in it until the onion is transparent. Add the bay leaf, thyme, parsley and lobster. Saute until the lobster turns red, or about five minutes, shaking the pan occasionally.
3. Add two tablespoons of cognac and ignite. Add the wine and stock and simmer twenty minutes.
4. Remove the lobster, cool and remove the meat from the shell. Dice the meat fine, add the sherry and set aside. Reserve the shell and broth.
5. Melt the remaining butter in a saucepan, add the flour and blend with a wire whisk. Meanwhile, bring the milk to a boil and add all at once to the butter-flour mixture, stirring vigorously with the whisk.
6. Grind or crush the lobster shell and add to the sauce. Add the reserved broth with the vegetables and simmer, covered, about one hour. Strain through a fine sieve.
7. Bring the sauce to a boil, and add enough cream to give the desired consistency. If desired, add a few drops of coloring to make the soup a delicate pink color.
8. Add the reserved lobster meat, correct the seasonings and add the remaining cognac.