In a large bowl, stir together the mashed potatoes, cheese, scallions, egg, and 3 tablespoons of the flour until fully combined.
Using your hands, divide the mixture into 12 portions. Roll each into a ball, then flatten into a pancake about 1/2-inch thick.
Place the remaining 1/2 cup of flour in a shallow dish and dredge each pancake on both sides.
Heat 3 to 4 tablespoons of vegetable oil in a large skillet over medium heat until shimmering.
Fry the pancakes in batches, 3 to 4 minutes per side, until golden brown and crisp. Add more oil between batches as needed. Avoid overcrowding the pan, and don't flip too early.
Transfer to a paper-towel-lined plate and sprinkle with salt immediately.
Serve warm, topped with sour cream and a few extra scallions if you like.