In a large bowl, mix together the mashed potatoes, eggs, cheese, and flour. Start with 6 tablespoons of flour, adding more if needed. You want a soft, slightly sticky dough that can be shaped into disks.

Using a cookie scoop, take balls of the potato mixture and flatten them into thick discs with damp hands. Keeping your hands a bit wet helps prevent the dough from sticking.

Heat the oil or nonstick cooking spray in a large frying pan over medium heat. Place the potato cakes in the hot pan and cook until golden brown on each side, about 3-5 minutes per side. Serve hot.