Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together half of the olive oil, lemon juice, lemon zest, minced garlic, dried oregano, sea salt, and black pepper to create a marinade.
Brush the salmon fillet and the trimmed asparagus spears with the remaining olive oil.
Place the salmon on the grill, skin-side down, and cook for approximately 4 to 5 minutes.
Add the asparagus spears to the grill alongside the salmon, turning occasionally to ensure even charring.
Carefully flip the salmon and grill for an additional 3 minutes, or until the fish flakes easily with a fork and the asparagus is crisp-tender.
While the salmon rests for a minute, stir the chopped fresh parsley into the plain Greek yogurt in a small ramekin.
Plate the grilled salmon and asparagus, topping the fish with the herbed yogurt sauce and a final squeeze of fresh lemon if desired.