Melt the butter on a hot grill or in a large skillet. Grill both slices of bread on one side.
At the same time, grill the corned beef in one stack and the sauerkraut in another. Cook until both are heated through.
Turn over one slice of the bread on the grill. Stack on the corned beef, top with the sauerkraut, then the cheese, and the second slice of bread, grill-side down. Continue to grill the Reuben until it's hot and melted, turning the sandwich over once. This usually takes place in 5 to 7 minutes.