Preheat oven to 450°F. Scrub potatoes and pat dry. Carefully cut each into 16 thin wedges. Place wedges in a large bowl. Pour olive oil over potatoes. Add salt, pepper, garlic and rosemary and toss to coat. Place Parmesan in a large bowl; set aside.
Arrange potatoes in a flat layer on 2 large rimmed baking sheets. Bake, turning once or twice, until lightly browned and soft in center, about 30 minutes.
Remove potatoes from oven and immediately toss with Parmesan in a bowl until coated. Serve hot.