Mix salt and water in a large bowl. Stir until salt is dissolved.
Submerge fish in the brine for 15 minutes.
Preheat oven to 475°F.
Remove fish from bowl and rinse under cold water; pat with paper towels until very dry.
Place fish, skin side up, on a cutting board. With a sharp knife, create four vertical slashes in the skin (but not deep enough to cut through). Set aside.
Heat 4 tablespoons olive oil in large ovenproof skillet over high heat. Add fish, skin side down. Sear until skin is crisp and brown, about 4 minutes.
Place skillet on the second shelf of the oven and roast fish until opaque in the center, about 4 minutes.
Serve with lemon and a side salad.