Preheat oven to 400°F. For each serving, cut a "lid" off a hard dinner roll. Pull out as much of the soft interior as you can. Put finely minced ham into the cavity. Carefully crack an egg on top of the ham. Put rolls on a baking sheet and bake in the oven for 5 to 7 minutes, or until the eggs have begun to set. Remove from oven and sprinkle each egg with salt and 2 tablespoons of shredded cheese. Return to oven and bake for 2 to 3 minutes more, or until the cheese has melted. Put the tops back onto the rolls and serve hot.