Place the asparagus in a single layer on a rimmed baking sheet and sprinkle with salt and pepper. Then drizzle olive oil over asparagus and toss to coat.
Transfer asparagus to the grill and cook for 5-10 minutes over medium high heat until they are fork tender and have char marks. Remove asparagus from grill and return to the baking sheet. Sprinkle on the garlic, Parmesan, lemon juice and zest; toss to coat.
Serve immediately. Top with a little bit of additional Parmesan or lemon zest, if desired.