Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together 1 teaspoon of olive oil, lemon juice, lemon zest, minced garlic, oregano, sea salt, and black pepper.
Brush the salmon fillet with the lemon-herb mixture on both sides.
Toss the asparagus spears with the remaining 1 teaspoon of olive oil and a small pinch of additional sea salt.
Place the salmon on the grill, skin-side down, and cook for 4-5 minutes.
Add the asparagus to the grill alongside the salmon during the last few minutes of cooking.
Flip the salmon carefully and grill for another 3-4 minutes until the fish is opaque and the asparagus is tender and charred.
Garnish with fresh parsley and serve immediately.