Place potatoes on a foil-lined rimmed baking sheet. In a small bowl, mash butter with garlic and oregano; season generously with salt and pepper. Using a vegetable peeler, shave Parmesan; slide between about half the potato slices. Brush some garlic-herb butter on top of the potatoes. Roast at 425 degrees , 10 minutes; brush with more garlic-herb butter. Roast until tender, about 10 minutes more. Broil until browned, 1 to 3 minutes. Season; brush with remaining garlic-herb butter.