In a mixing bowl, combine the cold mashed potatoes, shredded cheddar cheese, chopped green onions, all-purpose flour, breadcrumbs, beaten egg, salt, pepper, and any additional seasonings or herbs you desire. Mix well until all the ingredients are evenly incorporated and the mixture holds together.
Scoop about 1/4 cup of the potato mixture and shape it into a flat, round patty using your hands. Repeat the process with the remaining mixture until all the potato cakes are formed.
Preheat your air fryer to 375°F (190°C) for about 5 minutes.
Place the potato cakes in a single layer in the air fryer basket, leaving some space between each cake. Cook the potato cakes in the air fryer for approximately 10-12 minutes, flipping them halfway through the cooking process, until they turn golden brown and crispy on the outside.
Once the potato cakes are cooked to your desired crispiness, remove them from the air fryer and transfer them to a serving plate.
Serve the mashed potato cakes hot as a side dish or appetizer. You can serve them plain or with your favorite dipping sauce, such as sour cream, ketchup, or a spicy aioli.