Preheat your grill or grill pan over medium-high heat.
In a small glass bowl, whisk together the extra virgin olive oil, fresh lemon juice, lemon zest, minced garlic, chopped dill, and chopped parsley to create the marinade.
Pat the salmon fillet completely dry with a paper towel and season both sides with sea salt and black pepper.
Trim the woody ends off the asparagus and toss the spears with one teaspoon of the prepared marinade to coat lightly.
Brush the remaining marinade generously over the top and sides of the salmon fillet.
Place the salmon on the grill, skin-side down, and cook for 4 to 5 minutes without moving it to ensure a crispy skin.
Add the asparagus spears to the grill alongside the salmon, turning occasionally.
Carefully flip the salmon and grill for an additional 3 to 4 minutes until the fish flakes easily with a fork and the asparagus is tender-crisp with light char marks.
Remove from the heat and let the salmon rest for 2 minutes before serving.