Preheat the grill to medium-high heat.
Brush the salmon fillets with olive oil and sprinkle evenly with lemon pepper seasoning.
Place the salmon fillets skin-side down on the grill.
Grill for about 6 minutes per side, until the exterior is crispy and the interior is moist and flaky.
While the salmon grills, melt butter in a small saucepan over medium heat.
Add minced garlic and sauté for 1 minute until fragrant.
Stir in lemon juice and fresh parsley, cook for another minute. Remove from heat.
Once salmon is cooked, transfer to plates centered on each one.
Drizzle lemon pepper butter sauce over the salmon fillets.
Garnish with a lemon wedge on the side and sprinkle fresh parsley on top.
Serve immediately.