Preheat oven to 375 F and prepare a half sheet pan (about 13 x 18 inches) by lining with parchment paper. Place potatoes in a large bowl.
Combine the butter, olive oil, salt, pepper, garlic powder, and cayenne in a measuring cup or small bowl, then pour over the potatoes. Add the Parmesan and toss.
Spread the potatoes over the baking sheet in as thin a layer as possible. Then bake for 15 minutes. Remove from oven to quickly toss, then return to oven for another 15 minutes or so, just until crispy.