Place trimmed asparagus in a wide, shallow bowl. Drizzle with olive oil and balsamic vinegar and season with Mediterranean-spiced sea salt and black pepper. Gently toss to combine and set aside to marinate for 15-20 minutes.
While the asparagus marinates, prepare the gremolata by combining the parsley, lemon zest, preserved lemon rind, and garlic in a small bowl. Season with salt and black pepper to taste and set aside.
Spray grill grates with non-stick cooking spray and preheat to medium-high.
Thread several asparagus spears side by side onto two pre-soaked wooden skewers to keep them together and make turning easier.
Place the asparagus skewers and lemon halves over direct heat. Grill for 3-4 minutes per side, until crisp-tender with light char marks.
Remove from the grill and transfer to a serving dish. Top with gremolata and serve immediately with grilled lemon halves for squeezing and shaved Parmesan cheese if desired.