Pat the salmon fillets dry with paper towels.
In a small bowl, mix together lemon zest, black pepper, and kosher salt.
Rub the lemon pepper seasoning evenly over both sides of each salmon fillet.
Heat olive oil in a large non-stick skillet over medium-high heat until shimmering.
Place the salmon fillets skin-side down in the skillet and cook without moving for 5 to 6 minutes until the skin is crispy and the salmon is cooked about two-thirds of the way through.
Flip the salmon fillets carefully and add the minced garlic and butter to the skillet.
Spoon the melted butter and garlic over the salmon as it cooks for an additional 4 to 5 minutes, or until the salmon is cooked through and flakes easily with a fork.
Remove the skillet from heat and drizzle fresh lemon juice over the salmon fillets.
Transfer the salmon to serving plates and garnish with fresh lemon slices and chopped parsley.
Serve immediately.