Preheat your grill to medium-high heat. Brush the salmon fillets with olive oil and season them with salt and pepper.
Grill the salmon, skin-side down, for about 5-6 minutes. Flip carefully and grill for another 3-4 minutes or until the salmon is just cooked through and easily flakes with a fork.
While the salmon is grilling, prepare the lemon and parsley sauce. In a small bowl, whisk together the parsley, olive oil, lemon juice, garlic, salt, and pepper until well combined.
Once the salmon is cooked, remove from the grill and place on a serving platter. Drizzle the lemon and parsley sauce over the top of the salmon. Garnish with lemon slices before serving.
Tip:
For an extra flavor boost, let the salmon marinate in a portion of the lemon and parsley sauce for 30 minutes to an hour before grilling.