Preheat your grill to medium-high heat and lightly oil the grates to prevent sticking.
In a small bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, dill, and parsley until well combined.
Season the salmon fillet and the trimmed asparagus spears evenly with sea salt and black pepper.
Brush half of the prepared lemon-herb mixture over the salmon and the asparagus.
Place the salmon on the grill, skin-side down, and cook for approximately 4-5 minutes.
Add the asparagus spears to the grill alongside the salmon and cook for 3-4 minutes, turning occasionally until they are tender and slightly charred.
Carefully flip the salmon and grill for another 2-3 minutes until it reaches your desired level of doneness and flakes easily with a fork.
Remove the salmon and asparagus from the grill, drizzle with the remaining herb mixture, and serve immediately while hot.