Heat the pan: Heat the olive oil in a large skillet over medium-high heat. Season the salmon fillets with salt and pepper.

Sear the salmon: Place the salmon fillets skin-side down in the skillet. Cook for about 3-4 minutes on each side, or until the salmon is golden and cooked to your preferred level of doneness. Remove from the skillet and set aside.

Make the lemon butter sauce: In the same skillet, reduce the heat to medium and melt the butter. Add the minced garlic and sauté for about 1 minute, until fragrant. Stir in the lemon juice and lemon zest, cooking for another minute.

Return the salmon to the skillet: Place the salmon fillets back into the skillet and spoon the lemon butter sauce over the top. Let the salmon warm through in the sauce for 1-2 minutes.

Serve: Serve the salmon fillets hot, garnished with fresh parsley and lemon slices. Spoon extra lemon butter sauce over each fillet.