1. Make a bouquet garni by tying bay leaves, parsley, thyme, tarragon, dill, fennel seeds, and peppercorns in a piece of cheesecloth; set aside.

2. Melt the butter in the stockpot over medium-high heat. Add leeks, onion, mushrooms, carrots, celery, and fennel; cook until vegetables are tender, 8 to 10 minutes. Raise heat to high, and add fish heads and bones, wine, reserved bouquet garni, and enough water to just cover the bones (about 4 1/2 quarts). Bring mixture to a boil; reduce heat to medium-low, and simmer 25 minutes. Skim scum from surface with a large spoon, as needed.

3. Prepare an ice bath. Remove stockpot from heat, and strain stock through a fine sieve into a large heat-proof bowl set in the ice bath, and let cool slightly before using or storing.