Preheat oven to 400 F. Lightly grease a muffin or mini-muffin tin.
In a large bowl, whisk together the mashed potatoes, eggs, 3/4 cup of the grated cheese, chives, and bacon or ham, if using. Season with salt and pepper.
Spoon some of the potato mixture into each muffin cup, and sprinkle with the remaining grated cheese. Bake 20 minutes for mini-muffins, 30 for regular-sized ones, until the potatoes are set, golden brown, and heated through. Allow to cool for 5 minutes in the muffin tin, then use a sharp knife to gently lift the potato puffs out of the pan. Serve hot, with sour cream.