Pat the whiting fillets completely dry with paper towels. This is a crucial step for achieving a nice sear and preventing sticking.
Season both sides of the fillets generously with salt and pepper.
Heat the olive oil in a large non-stick skillet over medium-high heat until shimmering. If using butter and garlic, add the butter and minced garlic to the pan and swirl until the butter melts and garlic is fragrant, about 30 seconds, then proceed to add the fish.
Carefully place the whiting fillets into the hot skillet, presentation side down (usually the side without skin, if applicable). Do not overcrowd the pan; cook in batches if necessary.
Sear the fish for 3-4 minutes per side, or until golden brown and cooked through. The exact time will depend on the thickness of the fillets. The fish should flake easily with a fork when done.
In the last minute of cooking, squeeze the juice of half a lemon over the fillets. If you added garlic earlier, you can baste the fish with the pan juices.
Remove the whiting from the skillet and transfer to a serving platter. Garnish with fresh parsley and serve immediately with lemon wedges.