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1
Sweat the bones and vegetables Heat the oil in a medium stockpot over medium heat until hot but not smoking.
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2
Add fish parts, celery, and leek.
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3
Cover and cook, stirring once or twice, until vegetables are soft and translucent and flesh on the bones has turned opaque but not brown, about 3 minutes.
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4
Make stock Add wine and reduce by half, 3 to 5 minutes, then add enough water to cover by 1/2 inch (about 2 quarts) along with the bay leaf and peppercorns.
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5
Bring to just under a boil over medium-high heat, skimming foam with a ladle as it rises to the surface, then reduce heat and gently simmer (bubbles should just gently break the surface) for 35 minutes, skimming frequently.
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6
Strain stock Pass mixture through a fine sieve into a heatproof bowl or another pot (do not press on solids), discarding solids.
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7
Skim off fat.
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8
If not using immediately, let cool completely (in an ice-water bath, if desired) before transferring to airtight containers.
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9
Fish fumet can be refrigerated in airtight containers for up to 2 days or frozen for up to 3 months; thaw completely in the refrigerator before using.
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10
Ask your fishmonger to save the bones and heads from the fish in advance; firm-fleshed white fish, such as snapper, bass, and halibut, work best.
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11
Avoid oily fish (such as mackerel and tuna).