In a small 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 in a shallow dish and pour half of the marinade over it, ensuring it is well-coated; let it marinate for 15 minutes.
Preheat your grill or grill pan to medium-high heat and lightly grease the surface with a small amount of oil if necessary.
Toss the asparagus spears with the remaining marinade in a separate bowl until evenly coated.
Place the salmon on the grill skin-side down and cook for 4-5 minutes per side until the fish is opaque and flakes easily with a fork.
Add the asparagus to the grill during the last 5 minutes of cooking, turning occasionally until tender and slightly charred.
Remove the salmon and asparagus from the heat and serve immediately while hot.