Preheat your grill to medium-high heat, ensuring the grates are clean and lightly oiled.
In a small glass bowl, whisk together the extra virgin olive oil, fresh lemon juice, lemon zest, minced garlic, chopped dill, chopped parsley, sea salt, and black pepper.
Place the salmon fillet and the trimmed asparagus spears on a large tray.
Brush the lemon-herb marinade generously over both sides of the salmon and toss the asparagus to coat evenly.
Place the salmon on the grill skin-side down and cook for approximately 5 minutes without moving it to achieve a crisp skin.
Add the asparagus spears to the grill grates next to the salmon.
Carefully flip the salmon and grill for another 3 to 4 minutes, while turning the asparagus occasionally until tender and lightly charred.
Remove the salmon and asparagus from the grill once the fish flakes easily with a fork and serve immediately.