Remove haddock from the refrigerator and let stand for 10 minutes to take off the chill.

Pat each fillet completely dry with paper towels, then season both sides with sea salt and black pepper.

Spread the flour in a shallow dish and lightly dredge each fillet, shaking off excess so only a thin coating remains.

Heat a 12-inch skillet over medium-high heat for 2 minutes, add 2 tablespoons butter, and allow it to foam and turn lightly golden, about 1 minute.

Place the floured fillets in the skillet, skin-side up, and sear without moving for 4–5 minutes until a light golden crust forms.

Gently flip the fillets and cook the second side for 3–4 minutes, or until the fish flakes easily and registers 145°F in the thickest part. Transfer to a warm plate and tent with foil.

Return the skillet to medium heat, add the remaining 2 tablespoons butter and minced garlic (if using), and cook 30 seconds until fragrant.

Stir in lemon juice, half of the zest, and a pinch of salt and pepper; simmer 30 seconds, then spoon the sauce over the haddock. Garnish with parsley and the remaining zest; serve immediately.