Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, and dried oregano to create the marinade.
Place the salmon fillet and the trimmed asparagus spears on a large tray.
Brush the marinade generously over both sides of the salmon and coat the asparagus evenly.
Season both the salmon and asparagus with sea salt and black pepper.
Place the salmon on the grill, skin-side down, and cook for 5 minutes without moving it to ensure a good sear.
Add the asparagus to the grill and carefully flip the salmon fillet.
Grill for another 3 to 4 minutes until the salmon is opaque and flakes easily with a fork, and the asparagus is tender with light char marks.
Remove from the heat and garnish with freshly chopped parsley before serving.