Preheat your grill to medium-high heat and lightly oil the grates to prevent sticking.
Mince the garlic and finely chop the fresh dill and parsley.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dill, parsley, salt, and pepper.
Pat the salmon fillet dry with a paper towel and brush both sides generously with half of the herb mixture.
Toss the asparagus spears with the remaining herb mixture until evenly coated.
Place the salmon on the grill, skin-side down, and cook for about 4-5 minutes until the skin is crispy.
Carefully flip the salmon and add the asparagus to the grill; cook both for another 3-4 minutes until the salmon is flaky and the asparagus is tender-crisp.
Remove from the grill and let the salmon rest for 2 minutes before serving.