Preheat the grill to medium-high heat.
On a plate, roll the asparagus spears in olive oil and garlic until evenly coated.
Season with salt and pepper, to taste.
Once the grill is hot, place the asparagus directly on the grill grates in a single layer.
Grill the asparagus for 3-5 minutes, turning occasionally, until they are tender-crisp and have developed charred grill marks. Be sure to keep an eye on them to prevent burning.
Transfer asparagus to a serving platter.
To serve, sprinkle with grated Parmesan and lemon zest.