In a small bowl, mix the softened butter, grated Parmesan cheese, and grated garlic or garlic powder until well combined.
Spread a layer of the garlic butter mixture on one side of each slice of sourdough bread. On the unbuttered side of one slice, layer the mozzarella and white cheddar cheese, and top with the other slice of bread, buttered side facing up.
Place your skillet or griddle over medium heat and allow it to warm up for a minute or two.
Carefully place your sandwich in the skillet and cook for about 3-4 minutes on one side, or until golden brown and crispy.
Flip the sandwich using your spatula and cook for another 3-4 minutes until both sides are golden and the cheese is melted.
Remove the sandwich from the skillet, let it sit for a minute before slicing, and serve warm.