Pat the haddock fillets dry with paper towels. Inspect for any remaining bones and remove with kitchen tweezers. Place fillets on a plate and let sit at room temperature for 10 minutes.

Season both sides of the fillets evenly with kosher salt and freshly ground black pepper (about 1/2 tsp salt and 1/2 tsp pepper per fillet). Zest the lemon and reserve zest for the optional glaze; cut the lemon into wedges for serving.

Preheat oven to 400°F (205°C) if baking. If you prefer to pan-sear, heat a large oven-safe skillet over medium-high heat and add 1 tablespoon olive oil and 1 tablespoon butter.

Cook fillets (pan-sear then oven)

When the fat is shimmering, add the haddock fillets skin-side down. Cook undisturbed for 2–3 minutes until the skin is crisp and releases easily from the pan. Gently flip the fillets and cook the flesh side for 1 minute.

Transfer the skillet to the preheated oven and roast for 4–6 minutes, or until the fish flakes easily with a fork and reaches an internal temperature of 145°F (63°C). If you prefer to bake without searing: place fillets in a lightly oiled baking dish and bake 10–12 minutes until done.

Remove the skillet or baking dish from the oven. Add 1 tablespoon unsalted butter on top of the hot fillets and spoon melted butter over them once it melts. Sprinkle chopped fresh parsley and serve with lemon wedges.

Optional broiling finishing (broiled upon request)

If broiling is requested for a slightly crisped top, position the oven rack 6–8 inches from the broiler and switch the oven to Broil (high).

Combine the panko, grated Parmesan, reserved lemon zest, and a light drizzle (about 1 tsp) of olive oil. Mix with the 2 tbsp melted lemon-butter glaze to create a moist crumb topping.

Brush the tops of the cooked fillets with the lemon-butter glaze, sprinkle the panko-Parmesan mixture evenly over the fillets, and mist lightly with olive oil or spray.

Broil for 1–2 minutes, watching closely, until the topping is golden brown and crisp. Remove immediately to prevent overcooking. Spoon any accumulated pan juices over the fish and serve.