Preheat your grill or grill pan to medium-high heat.
Finely mince the garlic clove and roughly chop the fresh dill and parsley.
In a small mixing bowl, whisk together 1 tsp of olive oil, the lemon juice, lemon zest, minced garlic, chopped dill, parsley, sea salt, and black pepper.
Pat the salmon fillet dry with a paper towel and brush the herb mixture evenly over the top and sides.
Trim the woody ends off the asparagus and toss the spears with the remaining 1 tsp of olive oil and a tiny pinch of salt.
Place the salmon on the grill skin-side down and cook for 4 to 5 minutes without moving it to ensure a crisp skin.
Add the asparagus spears to the grill alongside the salmon.
Carefully flip the salmon and grill for another 3 to 4 minutes, or until the internal temperature reaches 145°F and the asparagus is tender with light char marks.
Remove from heat and let the salmon rest for 2 minutes before serving with the grilled asparagus.