Begin by patting the fish fillets dry with paper towels. Season both sides with salt and pepper.
On a plate, spread the flour evenly. Dredge each fish fillet in the flour, shaking off any excess.
In a large skillet, melt 2 tablespoons of butter over medium-high heat.
Carefully place the prepared fish fillets in the skillet. Cook for about 4-5 minutes on each side, or until the fish is golden brown and cooked through. The internal temperature should reach 145°F (63°C). Remove the fish from the skillet and transfer to a plate.
In the same skillet, add the remaining 2 tablespoons of butter. Once melted, add the minced garlic and sauté for about 30 seconds until fragrant.
Stir in the lemon juice and zest, allowing the sauce to simmer for 1-2 minutes.
Pour the lemon butter sauce over the cooked fish fillets.
Garnish with freshly chopped parsley before serving.