Immerse the salmon fillets in the cold brine for 15 minutes. Make the sauce while the salmon is in the brine.
Remove from the solution, pat to dry the excess moisture ensures that the fillets will cook to a golden brown.
Start the fillets skin side down in a cold oiled pan allows the interior to start cooking through gently; then, when the pan is fully hot, flip the fillets so that a crust can form on the flesh side and the fish can finish cooking through, about 10 minutes for a 1-inch thick fillet. Remove the skin.
Serve with steamed potatoes and beurre blanc.