Dissolve 1/2 cup salt in 8 cups water in a large container. Submerge salmon in brine and leave on the counter at room temperature for 15 minutes. Remove salmon from brine and pat dry with paper towels.
Sprinkle a 1/2 teaspoon salt and 1/2 teaspoon pepper in the bottom of a 12-inch nonstick skillet. Place fillets, skin side down, in cold skillet and sprinkle tops of fillets with a couple pinches of salt and pepper. Heat skillet over medium-high heat. Cook fillets without moving them until fat begins to render. The skin will just start to brown and the bottom ¼ inch of fillets turns opaque, 6 to 8 minutes.
Flip fillets with tongs and continue to cook without moving them, about 6 to 8 minutes more. Using the tip of a paring knife, check the fillet centers. They should be translucent and register 125 degrees or 120 degrees if cooking wild-caught salmon. Fillets should be golden brown and crisp on top. Transfer fillets skin side down to serving platter and let rest for 5 minutes. Or use a spatula to peel off skin before transferring to a warm platter. Serve with lemon wedges.
Notes
Adapted from Cook’s Illustrated.
Note: You don’t need oil in your pan for this recipe. The fat underneath the skin on the salmon fillet acts as the cooking medium.