Firstly, in a large bowl, stir together the mashed potatoes, cheese, scallions, egg, and 1.5 tablespoons of flour until well combined.
Next, using your hands, divide the mixture into 6 portions. Roll each portion into a compact ball then flatten it into a pancake about a 1/2-inch-thick.
Place the remaining flour in a shallow dish and carefully dredge each pancake in it before frying.
Heat 3 to 4 tablespoons of vegetable oil in a large sauté pan over medium heat. Keep in mind to add enough oil to thoroughly coat the bottom of the pan.
Just fry the pancakes, in batches, until they’re golden brown and crispy on both sides (for 3 to 4 minutes). Add more oil to the pan as needed between batches, do not overcrowd the pan, and do not flip the pancakes too soon if you want them to develop a crisp crust.
Finally, transfer the pancakes to a plate lined with a paper towel and immediately sprinkle them with salt.
I recommend serving the mashed potato pancakes topped with sour cream and garnished with additional chopped scallions.