Preheat oven to 350°.
Stir together egg, 3/4 cup milk, and bread; let stand for 5 minutes. Beat bread and milk mixture with a fork; stir in 1 teaspoon salt, 1/8 teaspoon pepper, nutmeg, onions, and ground beef. In a skillet, sauté sliced onions in hot oil until onions are golden and tender; remove onions with slotted spoon. Shape meatballs into balls with help from a teaspoon; drop into the hot fat. Brown quickly on all sides, then remove to a 1 1/2-quart casserole. Remove all but 2 tablespoons of fat from the skillet; place back on heat. Stir flour, 1/2 teaspoon salt, and 1/8 teaspoon pepper into the hot fat; stir until smooth and bubbly. Gradually stir in milk, cooking and stirring until thickened. Pour over meatballs then top casserole with sautéed onion slices. cover and bake for 30 minutes, until bubbly and hot. Serves 4.