In a bowl, combine butter, fresh parsley, garlic, salt, and dried oregano.
Brush the butter mixture on the cut sides of the two baguette halves. Sprinkle Parmesan cheese on both halves and top with mozzarella.
Place the baguette halves on a foil-lined grill. Cook on low heat for about 10 minutes until the cheese is melted. Cut into pieces and serve immediately.