Make the sauce: In a small saucepan over medium heat, add the oil and butter. Add the shallot and cook, stirring occasionally until soft, about 5 minutes. Stir in the lemon juice, capers, salt and pepper. Cook for one minute. Cover the pot and turn off the heat.
Pan-fry the fish: Meanwhile, heat an extra-large cast-iron or heavy-bottomed frying pan over medium-high heat. Rub a bit of the oil onto the skin side of each fish filet. Season both sides of each filet evenly with the salt and pepper. Place the fish filets skin-side-down into the pan, pressing gently on the tops of the filets with a spatula for about one minute to ensure that the filets do not curl up in the middle. Cook until the skin is well browned, 3 to 4 minutes. Using two spatulas, gently turn the filets over. Cook until just firm to the touch, about 2 to 3 minutes. Transfer the fish to a platter, skin-side up. Pour over the sauce and sprinkle with the chives. Garnish with the lemon wedges.
Makes 4 servings