Preheat your grill to medium-high heat and lightly brush the grates with a small amount of oil to prevent sticking.
In a small mixing bowl, whisk together the extra virgin olive oil, fresh lemon juice, lemon zest, minced garlic, chopped dill, chopped parsley, sea salt, and black pepper.
Brush half of the prepared lemon-herb marinade over the salmon fillet, ensuring it is evenly coated.
Toss the trimmed asparagus spears with the remaining half of the marinade in a separate bowl or tray.
Place the salmon on the grill, skin-side down, and cook for approximately 4-5 minutes without moving it to develop a good sear.
Add the asparagus spears to the grill grates next to the salmon.
Carefully flip the salmon and continue grilling for another 3-4 minutes, or until the fish reaches your desired level of doneness and flakes easily with a fork.
Grill the asparagus for the same duration, turning occasionally until they are tender and slightly charred.
Remove both the salmon and asparagus from the grill and serve immediately while hot.