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1.
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In a food processor or grinder, grind fish (refrigerate heads and bones for later use), 2 onions, 1 stalk celery, and half a carrot.
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(If you use a food processor, make sure you leave no large pieces of fish or bones; you may want to transfer the mixture, bit by bit, into a wooden bowl, and go over it vigorously with a hand chopper.)
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2.
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Place fish mixture in a large bowl, and add eggs, sugar, salt, pepper, and corn oil, mixing thoroughly with a wire whisk.
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Stir in matzo meal, and continue to mix until everything is thoroughly blended.
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Refrigerate for 1 hour or more (longer, even overnight, is better).
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3.
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Fill 2 large stockpots three-quarters full of water, and bring to a vigorous boil.
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In each, throw in half the fish heads and bones, 2 onions, half the celery, and a carrot.
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Divide batter into 12 patties of equal size.
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(Don't worry that your batter is a little loose; it has to be that way to keep your gefilte fish light.)
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Transfer each patty to a large cooking spoon, shape into an oval, and very gently lower it into the boiling water.
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Put 6 in each pot.
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Lower heat and simmer for 1 1/2 hours.
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4.
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Remove fish balls and carrots from pots, and refrigerate on a covered plate.
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Discard everything else.
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Serve chilled with red and/or white horseradish.
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Slice carrots for garnish.