Put some mozzarella slices between 2 slices of the bread, then butter the outsides of the bread liberally; repeat with the remaining mozzarella and bread. Put the sandwiches on the griddle, cover with a large pan or metal bowl and cook until brown on the bottom, 3 to 4 minutes. Flip the sandwiches, cover again and cook until brown on the other side, 3 to 4 minutes.
Cut each sandwich into 8 pieces so people can share, or cut in half and eat it all yourself.
Covering the sandwiches when they cook helps melt the cheese.