Position oven racks to the upper-middle and lower-middle position; heat oven to 475°.
Brush each side of the bread slices lightly with the melted butter and spread them out in a single layer over two baking sheets.
Toast the bread in the oven to a light golden brown, 10-15 minutes, rotating the baking sheets from top to bottom halfway through the baking time.
Assemble eight sandwiches, each filled with 1/2 cup of the shredded cheese, making sure that the more toasted-looking sides of the bread are facing outward.
Lay the sandwiches on a baking sheet and press lightly on each of them.
Cover the baking sheet tightly with foil and bake until the cheese is thoroughly melted, 5-10 minutes.
Make ahead--the bread can be toasted, wrapped tightly with plastic wrap, and kept at room temperature for up to 24 hours in advance.