In a small bowl mix together butter, olive oil, garlic, parsley, and parmesan cheese. Lightly butter 1 side of each slice of bread. Add one slice of provolone and one slice of white American on the top of a buttered slice of bread.
Place the remaining bread slice on each sandwich, butter side up.
Heat a griddle or large nonstick pan over medium heat.
Add the sandwiches and cook until golden brown on the bottom, flip and cook on the other side until golden brown and the cheese has melted.