To prepare potato pancakes, in a medium-sized mixing bowl with a rubber spatula combine leftover mash potatoes, egg, and flour. Gently mix together until completely combined. Season with salt and pepper if necessary (Place in refrigerator until ready to use).
In a large, nonstick, heavy-bottomed 12-inch sauté pan over medium heat, add 1 tablespoon olive oil. Allow the oil to heat for 1 minute. Divide potato mixture into four equal portions and spoon into the hot pan. Using the bottom of the spoon gently press the pancakes flat (1/4 inch thick). Cook for 1 1/2 minutes on each side. Remove from pan and place on kitchen paper until eggs are finished cooking.