Preheat the oven to 375ºF. Grease a non-stick muffin pan with cooking spray.
In a large bowl, stir together the mashed potatoes, egg, 3/4 cup cheddar cheese and 2 tablespoons chopped chives. Season the mixture with salt and pepper. Using an ice cream scoop, divide the potato mixture evenly into the prepared muffin pan, packing the potatoes down into each cup.
Bake the muffins for 30 to 35 minutes until golden brown and crisp around the edges. Remove the pan from the oven, top the muffins with the remaining 1/4 cup cheddar cheese and return them to the oven for 3 more minutes. Remove the muffins from the oven and allow them to cool in the pan for 5 minutes.
Transfer the muffins to a serving dish, top them with the remaining 1 tablespoon of chopped chives and serve immediately.