In a small bowl, mix softened butter (or mayonnaise) with garlic powder and dried oregano.
Spread the garlic butter evenly across one side of each slice of sourdough bread (these will be the outer sides that touch the skillet).
Lay two slices of bread, buttered-side down, on a clean cutting board.
Sprinkle half of the shredded mozzarella evenly over the bread slices.
Spoon 2 tablespoons of pizza sauce over the cheese layer, spreading gently with the back of a spoon (keeping it slightly away from the extreme edges).
Layer the pepperoni slices and a sprinkle of parmesan cheese over the sauce.
Top with the remaining shredded mozzarella (the two cheese layers act as glue to seal the bread and sauce). Place the remaining bread slices on top, buttered-side facing outward.
Heat a non-stick skillet or cast-iron pan over medium-low heat. Place sandwiches in the skillet.
Cover the skillet with a lid and cook for 3 to 4 minutes until the bottom bread is deeply golden brown and crisp.
Remove lid, carefully flip the sandwiches, and cook uncovered for another 2 to 3 minutes, pressing down lightly with a spatula, until the second side is golden and the cheese is fully melted and gooey.
Transfer to a cutting board, let rest for 1 minute, slice diagonally, and serve hot with extra warm marinara sauce for dipping.