Spread butter on one side of each slice of bread.
Place half of the bread slices, buttered-side-down, in skillet over medium-low heat.
Place two ounces cheese on each piece of bread, followed by two ounces ham.
Place remaining slices of bread on sandwiches, buttered-side-up.
Flip sandwiches when first side is browned; fry until second side is browned and cheese is melting.