1Make the salmoriglio: Whisk 6 tablespoons olive oil with 1/4 cup freshly squeezed lemon juice, the zest of 1/2 lemon, and 2 tablespoons hot water. Add 6 tablespoons chopped italian parsley, 2 teaspoons finely chopped garlic, and 2 tablespoons chopped fresh oregano (or 2 teaspoons dried oregano).
2Preheat a grill or broiler. Brush both sides of four 6- to 8-ounce swordfish fillets, each about 1 inch thick, with some of the salmoriglio and sprinkle sea salt and freshly ground black pepper on both sides. Grill or broil until the fillets are just cooked through, about 5 minutes per side.
3Transfer to a serving platter. Gently warm the remaining salmoriglio and spoon over the fish.