Preheat the oven to 425℉ and set the rack to the lowest position. Line a sheet pan with parchment paper or foil for easier clean up.
Cut about 1/2 inch off of the top of the garlic head. Place it on a small piece of foil. Drizzle about 1/2 teaspoon of olive oil over the cut side of the garlic. Lightly wrap it in the foil. Place it on the sheet pan and into the hot oven about 15 minutes before the potatoes go in.
Wash and dry the potatoes. Do not peel them. Cut them into quarters or about one-inch pieces. Place the cut potatoes into a large mixing bowl. Pour the remaining olive oil over and toss well to coat. Season with salt and pepper and toss well again.
Remove the hot tray with the garlic from the oven. Spread the potatoes on the tray in a single layer. Return it to the oven and roast the potatoes and garlic packet for 20-25 minutes, turning the potatoes once or twice so they brown evenly on all sides.
While the potatoes and garlic roast, combine the Parmesan cheese and minced rosemary in a small bowl.
After 20 minutes, when the potatoes are starting to turn golden, remove the garlic packet from the oven. Open it and let it cool for about 5 minutes. Then, carefully squeeze the soft garlic cloves into the bowl with the Parmesan cheese and minced rosemary. Using a fork, mash the ingredients together.
When the potatoes are crispy, golden, and tender remove them from the oven. Place them back in the mixing bowl. Sprinkle the Parmesan cheese mixture over the potatoes and toss gently to coat the potatoes with the cheese, garlic, and rosemary. Taste and add extra salt if needed. Serve immediately.
Notes
Keep a close eye on the potatoes after 20 minutes. They can go from golden to burnt quickly!The garlic will take about 35-40 minutes to roast and soften. Test it by inserting the tip of a sharp knife into one of the cloves. It should be soft and tender.If the roasted potatoes are too cool, the Parmesan cheese mixture will not melt. If this happens, put the seasoned potatoes back on the sheet pan and return them to the oven for about three minutes, or until the cheese is melty.