Arrange a rack in the middle of oven and heat to 400°F. Lightly coat the cups of a mini-muffin tin with cooking spray or butter.
Place the mashed potatoes, eggs, ¾ cup of the cheese, chives, and bacon or ham in a large bowl and stir to combine. Season, if necessary, with salt and pepper. The seasoning will depend on how seasoned your mashed potatoes were to begin with.
Fill each muffin cup with the mashed potatoes. Sprinkle the tops with the remaining ¼ cup cheese.
Bake until the potato cups are set, browned on top, and heated through, about 20 minutes. Let cool for about 5 minutes in the pan, then use a spoon or knife to gently release them from the pan. Serve immediately with dollops of sour cream, if desired.
