Place the mashed potatoes in a large bowl (I used leftover colcannon). Gently mix in the flour and beaten egg (and any additional ingredients if using).
Form mixture into 9 pancakes and place them on a plate. Cover and refrigerate the potato pancakes until ready to use.
In a large cast iron skillet or suitable frying pan, heat about ½ inch of oil over medium-high heat to 365F/185C degrees. Add 3 pancakes at a time to the hot oil, being careful not to crowd pan. Shallow fry for about 5 minutes on one side, then flip over and cook 5 minutes on the other side, until cakes are brown and crispy.
Remove the finished pancakes to a baking sheet lined with a cooling rack or paper towels and keep warm in a 200F/93C degree oven. Repeat process with remaining potato mixture until all the pancakes are made.
Sprinkle the pancakes with the chopped green onions and serve with sour cream, applesauce, etc.