Preparation: Begin by patting dry the salmon fillets with paper towels to remove excess moisture. Season both sides with salt and pepper, ensuring even distribution of flavor.

Dredging: Next, place the all-purpose flour in a shallow dish or plate. Dredge each salmon fillet in the flour, shaking off any excess to achieve a light coating.

Sautéing: In a large skillet, melt 4 tablespoons of butter over medium-high heat until it begins to foam. Carefully add the salmon fillets to the skillet, skin side down, and cook for about 3-4 minutes, or until golden brown.

Flip and Cook: Gently flip the fillets using a spatula and cook for an additional 3-4 minutes, or until the salmon is cooked through and flakes easily with a fork.

Finishing Touches: Once the salmon is cooked, transfer it to a serving platter. In the same skillet, add the remaining 2 tablespoons of butter and lemon juice. Cook for a minute, swirling the skillet to combine the flavors.

Serve: Pour the lemon butter sauce over the salmon fillets and garnish with chopped parsley for a pop of color and freshness.