Preheat your grill or grill pan to medium-high heat.
In a small bowl, mince the garlic and finely chop the fresh parsley.
Pat the salmon fillet dry with a paper towel and trim the woody ends off the asparagus spears.
In a shallow dish, whisk together the olive oil, dried oregano, minced garlic, sea salt, and black pepper.
Brush the herb oil mixture generously over both the salmon fillet and the asparagus spears.
Place the salmon on the grill skin-side down and cook for 4 to 5 minutes per side, or until the fish flakes easily with a fork.
Add the asparagus to the grill alongside the salmon and cook for 3 to 5 minutes, turning occasionally until tender-crisp with light char marks.
Remove from heat and immediately squeeze the fresh lemon juice over the salmon and asparagus.
Garnish with the chopped fresh parsley and serve while hot.