Preheat the grill or a cast-iron grill pan to medium-high heat.
In a small glass bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, chopped dill, and chopped parsley to create the marinade.
Season the salmon fillet and the trimmed asparagus spears evenly with sea salt and black pepper.
Brush half of the lemon-herb marinade over the flesh side of the salmon and toss the asparagus with the remaining half until well-coated.
Place the salmon on the hot grill, skin-side down, and cook for 4 to 5 minutes without disturbing it to develop a crisp skin.
Arrange the asparagus spears on the grill next to the salmon, turning them occasionally to ensure even charring.
Carefully flip the salmon and grill for an additional 3 to 4 minutes, or until the internal temperature reaches 145 degrees Fahrenheit and the fish flakes easily.
Remove the salmon and asparagus from the grill and serve immediately with an optional extra wedge of fresh lemon.