Pat the fish dry with paper towels and feel for any bones to remove. (If using thawed fish that was frozen, squeeze out any remaining liquid.) Use kitchen scissors to cut the cod into portion sizes if needed.
Season the cod with the salt and pepper. Place ⅓ cup of flour in a dinner plate. Dredge the fish in the flour so it's coated on both sides. Save the rest of the flour so you can use a little of it to thicken the sauce later.
Add the oil to a 12-inch, nonstick skillet and heat it on medium-high. When the oil is rippling hot, use a spatula to add the cod to the pan in a single layer, uncovered.
Sear the first side without moving it for 4 minutes for thick pieces, or three minutes for thin pieces. Wait until they're browned and move easily when you nudge them before flipping them. Flip over the fish carefully (it helps to use two spatulas) and sear the second side without moving it for another 4 minutes for thick pieces or 3 minutes for thin ones. (If the cod is really thick, you might need an extra minute.) To check for doneness, you can place a thick piece of fish on a plate and cut it open. The fish should flake easily and not look shiny inside. Remove the cooked cod to a platter.
Carefully add ¼ cup wine to the pan over medium-high heat (the wine will splash, so you might want to wear gloves.) Scrape up the bits of cod with a wooden spoon and boil the wine for one minute, until the liquid is reduced by half. Stir in 1 tablespoon of lemon juice. Boil the sauce for another minute.
In a liquid measuring cup, whisk ¼ cup of chicken stock with 1 tablespoon of the remaining flour. Pour this mixture into the pan and whisk to combine, letting it cook for a minute. Whisk in 2 tablespoons of butter until melted and combined into the sauce. Stir in the drained capers and cook for a minute. Turn off the heat.
Spoon the sauce onto the cod and add a squeeze of lemon juice on top of each piece. Garnish with chopped parsley and serve with extra lemon wedges.
Store leftovers in the refrigerator for 3-4 days. Reheat leftovers in the microwave.
Notes
For nicely browned, seared cod, the fish must not be wet. Don't rinse it, and use paper towels to absorb any liquid.
Use cooking oil with a high smoke point, such as canola, avocado oil or vegetable oil. Don't use olive oil, which has a lower smoke point and will burn.