In a large mixing bowl, combine the cold mashed potatoes, shredded cheese, flour, chopped green onions, and the beaten egg. Season with salt, pepper, and any optional additions like garlic powder, crumbled bacon, or diced bell peppers. Mix everything together until well combined.
Form the Patties:
Dust your hands with a little flour to prevent sticking. Take a portion of the potato mixture and shape it into a patty about 1/2 inch thick. Repeat with the remaining mixture, making sure all patties are of even thickness for uniform cooking.
Cook the Patties:
Heat the olive oil or butter in a large non-stick skillet over medium heat. Once the oil is hot, carefully place the patties in the skillet. Cook for 4-5 minutes on each side, or until they are golden brown and crispy. Work in batches if necessary to avoid overcrowding the pan.
Serving:
Once cooked, transfer the patties to a plate lined with paper towels to drain any excess oil. Serve hot as a side dish or a snack, accompanied by your favorite dipping sauce, such as sour cream or a spicy ketchup.
Storage:
Any leftover patties can be stored in an airtight container in the refrigerator for up to 3 days. Reheat in a skillet over medium heat until warmed through and crispy again.