In a large bowl, combine mashed potatoes, egg, flour, Parmesan, green onions, garlic powder, onion powder, salt, and pepper. Mix until well combined.
Form the mixture into 8 patties of equal size.
Heat oil in a large skillet over medium heat.
Cook the patties in batches for 3-4 minutes on each side until golden brown and crispy.
Transfer to a paper towel-lined plate to drain excess oil.
Serve warm with sour cream, ketchup, or your favorite dipping sauce.