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1
Remove the gills and any blood from the fish heads; thoroughly wash the bones, and cut them to fit in a 12-quart stockpot.
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2
Tie the bay leaves, parsley, thyme, tarragon, fennel seeds, and peppercorns in a small piece of cheesecloth to make a bouquet garni; set aside.
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3
Melt the butter in the stockpot over medium heat; add the leek, onion, mushrooms, carrots, celery, and fennel, and cook until tender, 8 to 10 minutes.
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4
Increase the heat to medium high, and add the fish heads and bones.
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5
Cook, stirring, for 3 to 5 minutes.
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6
Add the wine, bouquet garni, and 2 1/2 quarts water, just covering the bones.
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7
Bring to a boil, reduce heat to low, skim, and let stock simmer for 25 minutes.
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8
Turn off heat; let sit for 10 minutes.
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9
Prepare an ice-water bath.
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10
Strain the stock through a fine sieve into a large bowl; set the bowl in the ice bath to cool.
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11
Use within 1 day, or freeze up to 3 months.
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12
To infuse your fish stock with the flavors of the Mediterranean, add one or more of the following ingredients: 1/2 teaspoon crumbled saffron threads, 6 sun-dried tomatoes (not packed in oil), 1 1/2 teaspoons sweet paprika, 1/2 teaspoon toasted fennel or cumin seeds, 3 garlic cloves, 20 shrimp shells, or the zest of 1 orange.