In a large mixing bowl, combine mashed potatoes with egg, flour, olive oil, salt, and pepper. Add any optional seasonings or Parmesan cheese for extra flavor. Mix until the ingredients form a smooth mixture. Add more flour, 1 tablespoon at a time, if it is too soft to hold its shape.
Take a small handful of the potato mixture and shape it into a disc. Repeat with the remaining amount.
Heat a nonstick skillet, slightly greased or oiled. When hot, place the pancakes without overcrowding the pan. Cook over medium heat until the underside is golden, then flip with a spatula and cook on the other side.
Once they are cooked, remove from the skillet and place on a paper towel-lined plate to drain off any excess oil. Serve warm for breakfast, as a side dish or a snack, or for dinner.