Whisk together the mashed potatoes, eggs, 3/4 cup of the cheese, the chives, and ham. Season, if necessary, with salt and pepper. The seasoning will depend on how seasoned your mashed potatoes were to begin with. Mound a spoonful of the mixture in each muffin cup. Sprinkle the tops with the remaining 1/4 cup of grated cheese. Bake for 20 minutes, or until the potato cups are set, browned on top, and hot through.