Preheat oven to 425°F. Line a rimmed sheet pan with parchment and brush it lightly with olive oil.
Cut potatoes into 1-inch pieces. Rinse briefly, then pat very dry so they crisp well.
Toss potatoes with remaining olive oil, melted butter, cornstarch, garlic powder, onion powder, smoked paprika, salt, pepper, and red pepper flakes.
Sprinkle 1/2 cup of the Parmesan evenly over the prepared pan to form a cheesy base.
Arrange potatoes cut-side down on the cheese. Roast 30–35 minutes until deep golden and tender.
Loosen potatoes with a thin spatula, flip, and roast 5–10 minutes more to crisp the tops.
Transfer to a platter. Shower with remaining Parmesan and parsley. Rest 2 minutes, then serve hot.