Brine the salmon* (optional): In a shallow dish whisk together 4 cups room temperature water and 3 tablespoons kosher salt until it dissolves. Place the salmon in the water and wait for 15 minutes.
Preheat the broiler to high.
Place a large sheet of aluminum foil on a baking sheet and brush it with olive oil. Pat each piece of salmon dry and place it on the foil skin side down. Brush salmon with a bit of olive oil and sprinkle with ½ teaspoon kosher salt (evenly divided among the fillets) and fresh ground pepper.
Broil 4 to 5 minutes for very thin salmon or 7 to 10 minutes for 1-inch thick salmon, until it’s just tender and pink at the center (the internal temperature should be between 125 to 130 degrees Fahrenheit in the center). Serve spritzed with lemon wedges or with Lemon Caper Sauce (recommended).