Preheat oven to 450°F. Butter a deep casserole dish. Grate potatoes, preferably by hand. Grate onion. Add 3 beaten eggs. Mix the warm milk with the melted butter and add to the potatoes. Add salt and pepper. Pour into buttered casserole and bake at preheated 450°F for 15 minutes. Lower temperature to 350°F for 45–60 minutes until browned on top and solid in center. Cut into squares. Serves 6–8.