Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together 1 teaspoon of olive oil, lemon juice, lemon zest, minced garlic, dill, and parsley.
Pat the salmon fillet dry with a paper towel and season with half of the sea salt and black pepper.
Brush the herb marinade generously over the top of the salmon fillet.
Toss the asparagus spears with the remaining 0.5 teaspoon of olive oil and the remaining salt and pepper.
Place the salmon on the grill, skin-side down first, and cook for 4-5 minutes.
Carefully flip the salmon and grill for another 3-4 minutes until it reaches an internal temperature of 145°F and flakes easily.
While the salmon finishes, place the asparagus on the grill and cook for 3-5 minutes, turning occasionally until charred and tender.
Remove from heat and serve the salmon immediately with the grilled asparagus.