Preheat oven to 250°F. Place a wire rack inside a large rimmed baking sheet; set aside.
Spread ½ tablespoon butter on 1 side of each bread slice. Flip 4 bread slices buttered side down, and top each with ½ cup cheddar and ¼ cup Gruyère. Top with remaining 4 bread slices, buttered side up.
Coat a large nonstick skillet with cooking spray, and heat over medium. Sprinkle ⅓ cup Parmesan cheese in skillet in a shape slightly larger than bread slice. Place 1 sandwich in skillet on top of cheese mound, and cook until cheese in sandwich is starting to melt and Parmesan is lightly browned, 2 to 4 minutes. Transfer sandwich to prepared baking sheet, Parmesan side down.
Sprinkle another ⅓ cup Parmesan in skillet in a shape slightly larger than bread slice. Place cooked sandwich, buttered side down, on top of Parmesan; cook until cheese in sandwich is melted and Parmesan is lightly browned, 2 to 3 minutes. Transfer sandwich to prepared baking sheet; place in oven, and keep warm.
Repeat procedure with remaining 3 sandwiches and remaining 2 cups Parmesan. Serve hot.
