In a small bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, sea salt, and black pepper to create the marinade.
Place the salmon fillet in a shallow dish and pour half of the marinade over it, ensuring it is well-coated. Let it sit for 10 minutes.
Preheat your grill or grill pan to medium-high heat.
Toss the trimmed asparagus with the remaining marinade in a separate bowl.
Place the salmon on the grill, skin-side down, and cook for about 4-5 minutes. Carefully flip and cook for another 3-4 minutes until the internal temperature reaches 145 degrees Fahrenheit.
While the salmon is cooking, place the asparagus on the grill and cook for 5-6 minutes, turning occasionally until tender and slightly charred.
Remove the salmon and asparagus from the grill. Garnish with fresh chopped parsley and serve with lemon slices on the side.