Preheat grill or cast iron pan to medium-high heat.
Toss asparagus with olive oil, salt, and pepper. Grill for 3 to 5 minutes until slightly charred and tender.
Meanwhile, in small bowl, mix lemon zest, lemon balm, garlic, hazelnuts, and olive oil.
Transfer grilled asparagus to serving plate and top with lemon balm gremolata.