Brine the salmon: While the oven preheats, in a shallow dish stir 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 (this should be about the time it takes to preheat).
Bake*: Rub the bottom of a baking dish with olive oil. Pat each piece of salmon dry and place it on the pan. Sprinkle the salmon with ⅛ teaspoon kosher salt for each of the 4 fillets and fresh ground pepper. Cover pan with foil and bake the salmon for 10 minutes. Then remove the foil bake again for 3 to 6 minutes, depending on thickness, until just tender and pink at the center (the internal temperature should be between 125 to 130 degrees Fahrenheit in the center). A 1-inch thick fillet should cook in about 15 minutes total.
Serve: When the salmon is done, spoon the pesto over the salmon. Sprinkle it with chopped pine nuts and if desired, a bit of lemon zest. Serve immediately. (Leftovers can be stored refrigerated for 3 to 4 days.)