Fish heads, tails, and bones can be found at most fish counters. Use this recipe to make our Classic Fish Chowder.
Heat a 12-quart stockpot over low heat. Add oil, shallot, leeks, fennel, and celery, and cook, stirring frequently, until softened, about 30 minutes. (Do not let vegetables brown.)
Add fish heads, tails, and bones, and cook until just starting to release their juices, 10 to 15 minutes. Add peppercorns, bay leaf, coriander, and water to cover bones by 1 inch. Raise heat to high, and simmer, then immediately reduce heat to medium-low. Simmer gently for 30 minutes, skimming any foam that rises to the surface; discard foam. (A hard boil will break the fish apart and make your fumet cloudy and bitter.)
Turn off heat, and add tarragon, parsley, chervil, and chives. Cover, and let steep for 20 minutes.
Strain fumet through a fine sieve lined with cheesecloth set over a large container. Cover, and refrigerate for up to 1 day (or freeze for up to 3 months; thaw before using).
Cover and refrigerate for up to 1 day, or freeze for up to 3 months and thaw before using.