Preheat your grill or a heavy grill pan over medium-high heat.
Pat the salmon fillet dry with a paper towel to ensure a good sear and trim the tough, woody ends off the asparagus spears.
In a small bowl, whisk together the extra virgin olive oil, the juice from half a lemon, dried oregano, garlic powder, sea salt, and black pepper.
Brush the herb and oil mixture generously over both sides of the salmon fillet and toss the asparagus in the remaining marinade.
Place the salmon on the grill skin-side down and cook for approximately 4 to 5 minutes without moving it to develop a crust.
Add the asparagus spears to the grill alongside the salmon, turning them occasionally.
Carefully flip the salmon and grill for another 3 to 4 minutes until the fish is opaque and flakes easily with a fork.
Remove the salmon and charred asparagus from the heat, garnish with freshly chopped parsley, and serve with an extra squeeze of lemon if desired.