Preheat your oven to 425°F (220°C).
Place a potato on a cutting board. Place two chopsticks or skewers parallel to the potato, one on each side to prevent cutting completely through the potato.
Using a sharp knife, make slices across the potato about 1/8 inch thick, stopping at the skewers.
Repeat the cutting process with the remaining potatoes.
In a small bowl, mix the olive oil and melted butter together.
Place the potatoes on a baking sheet. Brush them with half of the olive oil and butter mixture, making sure to get some of the mixture into the slices.
Season the potatoes with salt and pepper to taste.
Bake in the preheated oven for 40 minutes.
Remove the baking sheet from the oven and re-brush the potatoes with the remaining oil and butter mixture, then sprinkle with Parmesan cheese and rosemary.
Return the potatoes to the oven and bake for an additional 15 minutes, or until the potatoes are crispy and golden brown.
Serve immediately as a delicious side dish.