Prepare a grill for indirect heat: If using a gas grill, turn all the burners on high, close the lid and heat until the internal temperature is 400°. For a two-zone grill, turn off one side. For a three-zone grill, turn off the center zone. If using a charcoal grill, remove the top rack and light the charcoal; when the charcoal is covered with ash, mound on one side of the grill. Return the top rack.
Pull out some of the bread from the bottom half of each roll, leaving a 1/2-inch border all around; place on separate large sheets of foil. Brush the cut sides of the rolls with the butter. Crack 1 egg into each bottom roll half; top each with a quarter of the cheese and ham. Gently set the roll tops in place. Loosely fold the foil over the sandwiches, crimping to seal.
Place the sandwiches on the unlit part of the grill, cover and cook until the egg whites are set but the yolks are still runny and the cheese melts, carefully opening the foil packets and using a knife to lift the ham to check to see if the eggs are done, about 20 minutes.