Place asparagus in a wide, shallow bowl and drizzle with olive oil and balsamic vinegar.
Season with Mediterranean-spiced sea salt and black pepper, to taste.
Gently toss to combine and set aside for 15-20 minutes to marinade.
Prepare the gremolata by combining all ingredients is a small bowl. Season with salt and black pepper, to taste, and set aside.
Spray grill grates with non-stick cooking spray and preheat grill to medium-high.
Place asparagus and lemon halves over direct heat and grill for 3-4 minutes per side, or until they are crisp tender.
Remove from heat and transfer to a serving dish. Top with gremolata and serve immediately with grilled lemons for squeezing and shaved Parmesan cheese, if desired.