Heat broiler. Rinse livers thoroughly, and cut away membranes and any extra fat. Cut beef liver into 1-inch pieces; chicken livers can remain whole. Place livers in a large baking pan and drizzle with 2 tablespoons oil. Broil 8 to 10 minutes (keep an eye on it to make sure it doesn't burn). Turn and broil until fully cooked and lightly browned on both sides, about 5 minutes more. Transfer to shallow bowl. Cover with plastic wrap and chill in refrigerator, about 30 minutes.
In a large skillet, heat 2 tablespoons oil and 2 tablespoons schmaltz, over medium heat. Add onions and cook, stirring occasionally, until deep golden brown, 20 to 30 minutes. Transfer to a shallow bowl. Cover with plastic wrap and chill in refrigerator, about 30 minutes.
In a food processor combine half the liver, half the onions, 2 hard-boiled eggs, 1 1/2 teaspoons schmaltz, 1 teaspoon salt, and 1/8 teaspoon pepper. Process until smooth. Repeat. Chill before serving.
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