Preheat your grill to medium-high heat and lightly grease the grates with a bit of oil to prevent sticking.
In a small bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, dill, parsley, sea salt, and black pepper.
Pat the salmon fillet dry with a paper towel, then brush half of the lemon-herb mixture over the flesh side of the fish.
Toss the trimmed asparagus spears with the remaining marinade until they are evenly coated.
Place the salmon on the grill skin-side down and cook for about 5 minutes until the skin is crisp and the fish releases easily from the grates.
Add the asparagus to the grill and cook for 4 minutes, turning occasionally, until they are tender and slightly charred.
Carefully flip the salmon and grill for another 2-3 minutes until it reaches your desired level of doneness, then remove both from the heat and serve immediately.