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 saut 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.
While pancakes are cooking prepare the turkey hash. Place a 10-inch, nonstick, heavy-bottomed fry pan over high heat. Add 1 tablespoon olive oil and heat 1 minute. Add onions and red bell pepper, and cook 2 minutes over high heat. Reduce heat to medium-high, add garlic and turkey, and cook for another 2 minutes. Add green onions and completely combine.
Place the same non-stick saut pan the potato cakes where cooked in over medium-low heat. Add 1 teaspoon olive oil and heat 1 minute. Gently crack 4 eggs into pan being careful not to break the yolk. Once all 4 eggs are in the pan reduce heat to low. Cook for 3-4 minutes for sunny side up.
While eggs are cooking, place potato pancakes on 4 separate places. Spoon turkey hash over potato pancakes evenly between the 4 plates. Once eggs have cooked, place over the hash and garnish with green onions.