I am completely baffled over this and hope you can answer this. You write, "...stir the butter with the shredded cheddar cheese just until combined. Spread the cheddar-butter on one side of each slice of bread; arrange them buttered side down on a work surface." This means you are putting the side of the bread that has all of the butter and the cheese DOWN ON THE WORK SURFACE. Why would you do that?
This is a melt, not grilled cheese.