Bring a pot of salted water to a simmer. Add potatoes and cook 10–12 minutes until just tender. Drain and let steam-dry for 1–2 minutes.
In a large bowl, combine Parmesan, panko, garlic powder, smoked paprika, salt, and pepper. Toss warm potatoes with olive oil (and melted butter if using).
Add potatoes to the bowl with the crust mixture and gently toss until evenly coated.
Preheat oven to 425°F (220°C). Arrange potatoes in a single layer on a rimmed baking sheet. Bake 20–25 minutes, flipping once, until golden and crisp.
Let rest 2 minutes, sprinkle with parsley and flaky salt if desired. Serve hot.
Notes
Use freshly grated Parmesan for the best browning and texture.
Pat potatoes dry after parboiling to help the crust adhere and crisp.
To reheat and restore crispiness, use an oven or air fryer rather than a microwave.
Parboil potatoes a day ahead and refrigerate to save time on the day you serve them.