Preheat the oven to 425°F and prepare a baking sheet by lining it with parchment paper.
In a large bowl, toss the halved potatoes with the melted butter, salt, and black pepper until evenly coated.
In a separate bowl, combine the grated Parmesan cheese, garlic powder, and dried oregano.
Dip the cut side of each potato into the Parmesan mixture, pressing gently to help the cheese adhere. Arrange the potatoes on the prepared baking sheet with the cheese-coated side down.
Brush any remaining butter over the tops of the potatoes and sprinkle any leftover cheese mixture across them.
Bake for 25-30 minutes, or until the potatoes are tender and the Parmesan crust is golden and crisp. Allow to cool for 2-3 minutes before using a spatula to transfer them to a serving plate.
Serve warm with your preferred dip.