Pat the salmon fillets completely dry with paper towels. This is crucial for getting a good sear. Season both sides generously with salt and black pepper.

Place a large non-stick skillet over medium-high heat. Add the olive oil. Once the oil is hot and shimmering, carefully place the salmon fillets in the skillet, skin-side up (if using skinless, either side is fine to start).

Sear for 4-6 minutes without moving the fillets, until a golden-brown crust forms on the bottom. You can see the color change up the side of the fillet.

Flip the salmon fillets using a fish spatula. Cook for another 2-4 minutes on the second side, or until the salmon is cooked to your desired doneness. Remove the salmon from the skillet and set aside on a plate.

Reduce the skillet heat to medium-low. Add the minced garlic to the same skillet and sauté for about 30-60 seconds until fragrant. Be careful not to let it burn.

Pour in the white wine (or chicken broth) to deglaze the pan, using a wooden spoon to scrape up any delicious browned bits from the bottom. Let it simmer for 1-2 minutes until it has reduced by about half.

Stir in the fresh lemon juice. Add the cubed butter, one piece at a time, swirling the pan continuously until the butter is completely melted and the sauce is smooth and slightly thickened.

Remove the skillet from the heat and stir in the chopped fresh parsley. Return the salmon fillets to the skillet, spooning the lemon butter sauce over them. Garnish with fresh lemon slices and extra parsley if desired. Serve immediately.