Heat the oil in a large soup pot set over high heat. Add the onions and saute until transparent, about 5 minutes. Add the fish steaks and sprinkle with half the salt and the juice of 1 lemon.

Cook for 5 minutes, then add enough water to barely cover the fish. Cover the pot and simmer over very low heat for 15 minutes.

While the fish is cooking, bring a saucepan of salted water to a boil over high heat and add the liver.

Cook it for 5 minutes, then drain and chop finely, or grind it in a food processor. Add one of the eggs, the matzo meal, parsley, remaining salt, and pepper; mix until smooth.

With hands dipped in matzo meal, shape the mixture into dumplings about 1 inch in diameter. Add the dumplings to the fish and cook, covered, at a bare simmer, for 15 minutes.

Carefully remove the fish and dumplings from the pot. Arrange the fish in the center of a serving platter and garnish with the dumplings.

Strain the liquid in which the fish was cooked. Combine the cornstarch with the juice of the remaining lemon, then add 2 cups of the cooking liquid. (If there is not enough liquid to make 2 cups, add water.)

Pour the liquid into a saucepan and bring it to a boil over high heat, stirring constantly. Cook for 3 minutes, then remove the pot from the heat.

Beat the 2 remaining eggs, then gradually add some of the cooking liquid, beating constantly to prevent curdling.

Return liquid to the pot, set over low heat, and stir constantly until sauce thickens; do not let it boil, or sauce will curdle.

Pour the sauce over the fish. Serve warm or cold.