Pat the salmon fillets dry with paper towels, then season on both sides with the salt and several grinds of black pepper.

Melt 2 tablespoons of the unsalted butter in a 10-inch nonstick skillet or well-seasoned cast iron skillet over medium heat. Add the salmon skin-side up and sear until golden brown, about 3 minutes. Flip and continue to cook until the skin is lightly crisp, about 3 minutes more.

Transfer the salmon skin-side down to a plate. It may not be cooked through, and that’s okay—it will finish cooking in the sauce.

Add the garlic to the pan and sauté until fragrant, less than 1 minute. Pour in the white wine and simmer, scraping up any browned bits on the bottom of the pan with a wooden spoon, until just slightly reduced, about 1 minute.

Reduce the heat to medium-low. Add the lemon zest and juice, capers, Dijon, and remaining 2 tablespoons butter. Stir to combine and melt the butter. Taste and season with salt and pepper as needed.

Return the salmon skin-side down to the pan. Simmer until just cooked through and an instant-read thermometer inserted into the thickest part of the salmon registers 120°F to 130°F (for medium-rare), 1 to 2 minutes. If you like your salmon medium-well or well-done, cook for a few minutes longer. Garnish with the parsley, if desired.