In a large bowl, combine mashed potatoes, flour, egg, cheese, green onions, salt, and pepper.
Form the mixture into small patties, about 2 inches in diameter.
Heat vegetable oil in a large skillet over medium heat.
Fry the potato cakes in batches until golden brown, about 3-4 minutes per side.
Once cooked, remove the cakes from the skillet and drain on paper towels.
Serve warm with your choice of dipping sauce or toppings.