In a small bowl, whisk together the extra virgin olive oil, fresh lemon juice, lemon zest, dried dill, dried parsley, sea salt, black pepper, and minced garlic to create the marinade.
Place the salmon fillet and the trimmed asparagus spears in a shallow glass dish or a large zip-top bag, ensuring they are not overcrowded.
Pour the marinade over the salmon and asparagus, turning them to ensure every surface is well-coated, then let them marinate for at least 15 minutes in the refrigerator.
Preheat a grill or a cast-iron grill pan over medium-high heat and lightly grease the grates with a high-smoke-point oil if necessary.
Place the salmon on the grill, skin-side down, and cook for about 5 minutes until the skin is crispy and the fish releases easily from the grates.
Flip the salmon carefully and add the asparagus spears to the grill; cook the salmon for another 3-4 minutes and the asparagus for 5-6 minutes until tender and slightly charred.
Remove the salmon and asparagus from the heat and serve immediately, garnishing with fresh lemon slices or extra herbs if desired.