Adapted from Martha Stewart
Preheat oven to 475 degrees. On a rimmed baking sheet, combine turnips, cayenne, nutmeg, and oil. Season with salt and pepper and toss well to coat. Sprinkle with Parmesan and toss gently to combine. Arrange turnips in a single layer and roast until golden on both sides, 25 to 30 minutes, flipping halfway through.