Place the softened butter, garlic, and Parmesan in a small bowl and mix well with a fork until evenly combined.
Spread the garlic butter on one side of each slice of bread.
Heat a skillet on medium low.
Place one slice of bread buttered-side-down in the skillet.
Arrange 2 slices each of mozzarella and cheddar on the slice of bread.
Top with another slice of bread, buttered side up.
Cook for 3-4 minutes per side, pressing the sandwich gently with a spatula to help the cheese adhere, until the cheese is completely melted and the bread is crispy and browned. Repeat steps 4-7 to make th second sandwich.