Heat the oil in a heavy stockpot.
Add the onion and cook over low heat until it is soft but not brown, about 8 minutes.
Stir in the celery and carrot and cook 5 minutes longer.
Stir in the lobster heads and shells and the wine and cook until nearly all the wine has evaporated.
Add the cognac and cook until it has evaporated.
Stir in the fish stock and simmer 30 minutes, skimming the surface as needed.
Strain, allow to cool to room temperature, then refrigerate or freeze.