Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dill, and parsley.
Season the salmon fillet with sea salt and black pepper, then brush half of the lemon-herb mixture over the top.
Toss the asparagus spears with a tiny drop of oil and a pinch of salt.
Place the salmon on the grill, skin-side down first, and cook for 4-5 minutes.
Flip the salmon carefully and grill for another 3-4 minutes until it flakes easily with a fork.
Grill the asparagus simultaneously for 5-6 minutes, turning occasionally until tender and slightly charred.
Drizzle the remaining herb mixture over the cooked salmon before serving.