In a small bowl, combine the softened butter, finely grated Parmesan cheese, and grated garlic (or garlic powder). Mix well until all ingredients are thoroughly combined.
Take two slices of sourdough bread and spread a generous amount of the garlic butter mixture on one side of each slice. On the non-buttered side of one slice, layer the mozzarella and white cheddar cheeses. Top with the second slice of bread, buttered side up.
Place your skillet or frying pan over medium heat. Allow it to warm up for a minute or two.
Carefully place the assembled sandwich into the hot skillet. Cook for about 3-4 minutes until the bottom is golden brown. Using your spatula, gently flip the sandwich and cook the other side for another 3-4 minutes.
Once both sides are golden and the cheese is melty, remove the sandwich from the skillet and let it cool for a minute. Slice in half and serve immediately.