Preheat Oven: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease it.
Prepare the Parmesan Mixture: In a small bowl, mix together the grated Parmesan cheese, garlic powder, onion powder, dried thyme, paprika, salt, and black pepper.
Prepare the Potatoes: Brush the cut sides of the potato halves with the melted butter. Sprinkle the Parmesan mixture generously over the cut sides, pressing gently to adhere the mixture to the potatoes.
Arrange the Potatoes: Pour the olive oil onto the prepared baking sheet and spread it out evenly. Place the Parmesan-coated potatoes cut side down on the baking sheet.
Bake: Bake in the preheated oven for 35-40 minutes, or until the potatoes are tender and the Parmesan crust is golden and crispy.
Serve: Remove the potatoes from the oven and let them cool slightly. Garnish with fresh chopped parsley if desired. Serve warm.