Heat an 8-quart stockpot over high heat for about 2 minutes. Add the olive oil and lobster and saute until the shells turn bright red.
Remove the pan from the heat, add the Cognac, then return to the heat and allow the alcohol to burn off, about 15 to 20 seconds. Add the tomatoes and tomato paste and stir. Add the remaining ingredients and cover with cold water.
Bring to a boil over high heat, skim, and reduce the heat. Simmer gently for 1 to 1 1/2 hours. Cool slightly and strain through a fine sieve.
The stock will keep for 2 to 3 days in the refrigerator, or freeze in 1-cup batches.
You can substitute shrimp shells for the lobster heads. The more you use, the richer the stock will be. When cooking shrimp or lobsters, simply reserve the shells or heads as the case may be and freeze them so you will have them available to prepare this stock.