Melt the butter in a small saucepan over low heat. Once melted and separated, set aside the clear gold liquid (clarified butter) and discard the white milk solids.
Season the salmon with salt on both sides.
Place a cast-iron skillet over medium-high heat. Add enough clarified butter to coat the bottom of the skillet. Once the butter is hot, add the salmon fillets. Leave the salmon alone for 3 to 4 minutes to allow a golden-brown crust to form; moving it too early may cause it to stick.
Using a fish spatula, carefully flip the salmon fillets. Immediately add the remaining clarified butter and 1 tablespoon of lemon juice to the pan. As the butter bubbles, use a spoon to continuously baste the salmon with the lemon butter for an additional 2 to 5 minutes, depending on the thickness of the fish.
Transfer the salmon to a serving plate and drizzle any remaining lemon butter from the skillet over the top. Sprinkle with the remaining tablespoon of lemon juice and the minced parsley. Sprinkle with black pepper if desired. Serve with fresh lemon wedges.
Recipe Tips
Atlantic salmon works best for this recipe due to its higher fat content and buttery flavor.
Don't skip clarifying the butter. Regular butter will burn at the high heat needed for proper searing.
A cast-iron skillet holds heat better than stainless steel, creating superior browning.
The salmon is done when it flakes easily with a fork and reaches 125-130°F for medium or 145°F for well-done.