Prep the asparagus. Look for asparagus that's bright green and slightly larger than pencil thickness.Discard any discolored or wilted asparagus and rinse them under cold water. Pat them dry, then discard the woody ends by slicing or snapping them off. You'll want to cut off 1 1/2-2 inches off the bottom of the asparagus, on average. Place the asparagus in a shallow bowl or baking dish.
Make the marinade/dressing. In a small bowl, whisk together the olive oil, lemon zest, lemon juice, garlic, and rosemary together. Season with salt and pepper. Pour 2/3 of the marinade over the asparagus and toss well to coat. Let the asparagus marinate while you prep and preheat the grill.
Prep and preheat the grill. Before using your grill, make sure to clean the grates of any food and debris. Lightly grease the grates with nonstick spray. Preheat your grill to medium-low heat. If you’re using charcoal, move all the hot coals to one side. Close the lid and wait at least 15 minutes, until the temperature reaches 450 F.
Grill the asparagus. Place the asparagus across the grill grates perpendicular to the bars. Grill with the lid closed for 5-7 minutes or until the spears are tender and crisp. Use tongs to roll the spears for even grill marks.
Dress and serve the asparagus. Transfer the asparagus back to the container they marinated in and toss with the remaining lemon dressing. Lay them on a serving tray and top with the parmesan cheese.