Prepare the mashed potatoes: If using leftover mashed potatoes, place them in a large bowl and break up any large clumps. If using freshly made mashed potatoes, let them cool slightly so they’re easier to work with.
Mix the binding ingredients: Add the egg, flour, garlic powder, salt, and black pepper to the potatoes. Stir until combined. If the mixture feels very wet, add a tablespoon of flour at a time until it holds together but remains slightly soft.
Fold in flavor: Fold in the chopped green onions and grated cheddar (if using). Taste a small amount and adjust seasoning if needed — a pinch more salt or pepper can make a big difference.
Form the cakes: Scoop about 1/3 cup to 1/2 cup of the mixture and shape it into a patty about 1/2-inch to 3/4-inch thick. Press gently to compact it so it won’t fall apart in the pan. Place on a plate and repeat until all mixture is used.
Heat the pan: Warm a large nonstick or cast-iron skillet over medium heat. Add the oil and swirl to coat the surface — you want a thin, even layer of oil so the cakes crisp without absorbing too much fat.
Fry until golden: Add the patties to the hot pan without crowding (work in batches if needed). Cook 3–4 minutes per side, or until a deep golden-brown crust forms. Flip carefully with a spatula to avoid breaking the cake.
Drain and rest: Transfer cooked cakes to a plate lined with paper towels to absorb excess oil. Let them rest 1–2 minutes; they’ll firm up slightly as they cool.
Serve warm: Garnish with fresh herbs or a light dusting of paprika. Serve with a dollop of sour cream, applesauce, or your favorite dipping sauce.