1. In a heavy 10- to 12-inch skillet, heat the oil over high heat until a light haze forms above it. Drop in the calf or beef liver and, stirring constantly, fry until the pieces are golden brown. With a rubber spatula scrape the liver into a mixing bowl.
2. Melt the 2 tablespoons of butter in the same skillet and add the carrot and onions. Cook uncovered over moderate heat, stirring occasionally, until the vegetables are soft but not brown, then add them to the liver in the bowl. Stir in the chopped parsley and put the entire mixture through the finest blade of a meat grinder.
3. With a large spoon, beat in the salt, pepper and nutmeg, then beat in the 8 tablespoons of butter, 1 tablespoon at a time. Puree the mixture through the finest blade of a food mill and taste for seasoning.
4. Spoon the pate into a 1-to 1½-quart mold, smooth the top and cover with plastic wrap. Refrigerate for at least 8 hours, or until firm.
5. Serve the pate directly from the mold or, if you prefer, unmold the pate in the following fashion: Run a knife around the edge of the mold and invert a flat plate on top.
6. Grasp the plate and mold firmly together and turn them over. The pate should slide out easily. Surround the pate with the hard cooked egg halves and serve as an appetizer.
