Mix beaten egg with leftover mashed potatoes - they must be cold.
Form the potatoes into flat cakes 3 to 4 inches across and 1 to 1-1/2 inches thick. Brush with butter and sauté gently in butter till the cakes are nicely browned on both sides.
For 4 potato cakes you will need about 2 cups mashed potatoes, 1 egg and 6 tablespoons butter. Serve very hot. Excellent with chops, steak, or cold meat.