Heat oven to 425º F. Place the asparagus on a rimmed baking sheet. Drizzle with the oil and shake the pan to coat the asparagus. Season with the salt and pepper. Roast, shaking the pan occasionally, until the asparagus are tender, 7 to 10 minutes (depending on the thickness). Remove from oven.
Heat broiler on high. Sprinkle the Parmesan over the asparagus. Broil until crisp and golden, 2 to 3 minutes. Serve immediately.