Preheat the grill or grill pan to medium-high heat.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, and dried oregano.
Season the salmon fillet and asparagus spears with sea salt and black pepper.
Brush half of the lemon-herb mixture over the salmon and asparagus spears.
Place the salmon on the grill, skin-side down, and cook for 4-5 minutes.
Place the asparagus on the grill next to the salmon and cook, turning occasionally.
Flip the salmon carefully and cook for another 3-4 minutes until the internal temperature reaches 145 degrees Fahrenheit and the asparagus is tender-crisp.
Remove from heat, drizzle with the remaining herb mixture, and garnish with fresh parsley.