1. In a large bowl, stir together the mashed potatoes, cheese, scallions, leftovers, egg and 3 tablespoons flour until combined. If the mixture is too wet, continue adding flour tablespoon by tablespoon until it’s dry enough to form into cakes.
2. Roll small portions of potato between your hands, then flatten until they’re about ½ inch thick.
3. Place cornstarch in shallow dish and dredge potato cakes on both sides.
4. Heat cast-iron pan until very hot, then add a few tablespoons of vegetable oil (enough to completely coat the bottom of the pan).
5. Fry potato cakes in batches until golden brown and crisp on both sides, about 3-4 minutes. Add more oil to the pan in between batches as needed. Don’t flip the cakes too soon or they won’t develop a good crust.
6. Season with salt as you remove the potato cakes from the pan.
7. Top with fried eggs, leftover gravy, sour cream, etc.