Preheat your grill or a heavy 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.
Place the salmon fillet and the trimmed asparagus spears on a large plate or tray.
Brush half of the prepared lemon-herb marinade over the salmon and the asparagus, ensuring they are evenly coated.
Season both the salmon and the asparagus with the sea salt and black pepper.
Place the salmon on the hot grill, skin-side down, and cook for approximately 4 to 5 minutes without moving it to develop a good sear.
Add the asparagus spears to the grill alongside the salmon and cook for 4 to 5 minutes, turning occasionally until they are crisp-tender and show light char marks.
Carefully flip the salmon and grill for another 3 minutes until the fish is cooked through and easily flakes with a fork, then remove everything from the heat and drizzle with the remaining marinade before serving.