Arrange 4 ounces Havarti or Swiss cheese on the bottom half of the rolls in an even layer. Top with 12 ounces sliced turkey, folding the slices into quarters before placing them onto the rolls. Top with the remaining 4 ounces cheese. Close with the top half of the rolls, mayonnaise-side down. Brush the tops of the rolls with the melted butter mixture, using it all. Cover the baking dish tightly with aluminum foil.