Preheat grill to medium-high heat.
Mince the garlic and finely chop the fresh parsley.
In a small bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, sea salt, and black pepper.
Trim the woody ends off the asparagus spears and place them in a shallow dish.
Brush the salmon fillet and the asparagus spears generously with the lemon-herb mixture.
Place the salmon on the grill, skin-side down, and cook for 4-5 minutes.
Add the asparagus to the grill grates alongside the salmon, turning occasionally.
Carefully flip the salmon and grill for another 3-4 minutes until the fish flakes easily and the asparagus is tender with light char marks.
Remove from heat and garnish with fresh parsley before serving.