Crack lobster claws and cut body and tail into four or five pieces. Saute diced carrots and onion with 2 tablespoons butter for 5 minutes. Add bay leaf, thyme, parsley and lobster. Cook until lobster turns red, about 5 minutes. Add 2 tablespoons cognac and ignite. Add white wine and broth. Simmer 20 minutes. Remove meat from lobster, reserving shells and broth.
Melt 3 tablespoons butter in a saucepan. Add flour. Cook, stirring constantly for 2 minutes. Add 3 cups boiling milk all at once and whisk until smooth. Crush lobster shells and add to sauce. Add reserve broth with vegetables and simmer, covered, 1 hour. Strain through a sieve. Heat to boiling and add 3 tablespoons cream. You can add a few drops of red food coloring to give it that lovely pink color, if you wish. Add the lobster, before serving, plus remaining cognac.
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