Preheat a griddle pan or skillet over medium heat. Place hot dogs cut-side down on the griddle and cook until brown. Flip and brown on the other side.
 
Butter the outsides of each hot dog bun. Put 2 slices of American cheese inside each bun and nestle the griddled hot dogs on top of the cheese. Place hot dogs on the griddle or skillet and cook like a grilled cheese until cheese is melted.