In a large bowl, combine the cold mashed potatoes, 1/2 cup of shredded cheese, the beaten egg, and a pinch of salt and pepper. Mix until well combined. If the mixture is too wet, add 1-2 tablespoons of flour or a bit more cheese to firm it up.

Take small portions of the mashed potato mixture (about 1-1.5 tablespoons each) and roll them into balls, small cylinders, or flatten them into disc shapes. Once shaped, you can begin to bread them.

Prepare three shallow dishes for the breading station. In the first dish, place the all-purpose flour; in the second, the remaining beaten egg (you might need another if making a large batch); and in the third, place the breadcrumbs.

Gently roll each potato bite first in the flour, shaking off any excess. Dip it into the egg, ensuring it's fully coated and letting any excess drip off, then roll generously in the breadcrumbs, pressing lightly for an even coating.

Choose your cooking method. For frying, heat 1-2 inches of vegetable oil in a deep skillet to 350-375°F (175-190°C), then fry in batches for 3-5 minutes until golden brown and crispy, draining on paper towels. For baking, preheat the oven to 400°F (200°C), arrange bites on a greased baking sheet, and bake for 20-25 minutes, flipping halfway, until golden and crispy.

Serve your crispy mashed potato cheese bites hot, optionally with a dipping sauce.