Preheat the oven to 400 degrees F.
Place the cheese mixture and garlic in the bowl of a stand mixer fitted with the paddle attachment and mix to combine. Using your hands, roll the mixture into a ball.
Spread the butter on one side of each slice of bread.
Spread the cheese mixture on the unbuttered side of one of the slices of bread and place the other slice on top, butter-side up. Press the Parmesan into the butter.
Place the sandwich Parmesan-side up in a heated oven-safe nonstick pan and place the pan in the oven. Cook until the sandwich is browned on both sides, 6 to 7 minutes.