How to Make It
Sprinkle fillets with pepper and 3/4 teaspoon salt; let stand 20 minutes.
Heat a large nonstick skillet over medium-high. Add lemons, cut sides down, and cook until lightly charred, about 5 minutes. Add olive oil, and place fillets, skin sides down, in skillet with lemon. Cook, undisturbed, until sides of skin begin to brown and fish is almost fully opaque, 5 to 7 minutes.
When the fillets appear to be approximately 90% cooked through, gently shake skillet. When cooked with patience, the fish will release itself from the pan, allowing you to flip the fillets without sticking. Flip fillets, and cook 1 minute. Transfer fish and lemons to plates. Cut each lemon half into 2 wedges. Wipe skillet clean.
Reduce heat to medium-low, and add wine, remaining 1/4 teaspoon salt, and butter. As butter melts, whisk to emulsify mixture. Spoon sauce over fillets. Sprinkle with parsley, and serve with a charred lemon wedge.