Mix together mashed potatoes, beaten egg and onion in a medium bowl. Add salt and pepper and stir. Over medium heat, heat olive oil in a non-stick frying pan. Drop about 1/4 cup of the potato mixture into the frying pan, patting it into 4 inch circles that are 1/2" thick. Cook until bottom is browned and crisp, about 3-4 minutes. Carefully turn the patty over and cook the second side until brown and crisp, 3-4 minutes.
You may enjoy these with ketchup or salsa.