Gather your cold leftover mashed potatoes. If they are very loose, you can reduce moisture by stirring in a handful of breadcrumbs or letting them sit in a fine mesh sieve for a few minutes.

In a mixing bowl, combine the mashed potatoes, egg, grated cheese (if using), chopped green onions, salt, and pepper. Mix until evenly combined. The mixture should hold together when pressed; if too wet, add a little flour or breadcrumbs.

Form the potato mixture into patties — about 8 medium or 4 large. Press them firmly so they will hold their shape when frying.

Lightly dredge each patty in extra flour or panko. This helps create a golden crust.

Heat a large skillet over medium heat and add butter or oil. Once hot, place the patties in the pan without crowding. Fry for 3 to 4 minutes per side, or until deep golden and crisp.

Transfer to a paper towel–lined plate to drain briefly. Serve hot with sour cream, applesauce, ketchup, or your favorite dipping sauce.

Leftovers can be reheated in a skillet or oven to keep the crust crisp. Avoid microwaving for too long or the crust will soften.