1. Pat the flounder fillets dry very well with paper towels. This helps the flour coating adhere and promotes light browning.

2. Season both sides of the fillets lightly with sea salt and black pepper.

3. Place the flour in a shallow dish and season it with a pinch of salt and pepper. Dredge each fillet in the flour, shaking off any excess. The coating should be light and even.

4. Heat a large skillet over medium to medium-high heat. Add 1 tablespoon of olive oil and 2 tablespoons of the butter.

5. Once the butter is melted and foamy but not browned, add 2 of the floured fillets to the pan (do not overcrowd). Cook for about 2–3 minutes per side, or until lightly golden and just cooked through. Transfer the cooked fish to a warm plate and tent loosely with foil.

6. Add the remaining 1 tablespoon olive oil and another 2 tablespoons butter to the pan. Repeat with the remaining fillets, cooking until golden and opaque in the center. Transfer to the plate with the other fish and keep warm.

7. Lower the heat to medium-low. Add the remaining 2 tablespoons butter to the same skillet. Let it melt and cook, swirling the pan often, until the butter turns a light golden brown and smells nutty. Watch closely so it does not burn.

8. Once the butter is browned, remove the pan briefly from the heat and carefully stir in the fresh lemon juice. The mixture will bubble. Return to low heat if needed and scrape up any browned bits from the bottom of the pan.

9. Stir in the chopped fresh parsley and taste the sauce. Adjust with a pinch more salt and black pepper if needed.

10. Place the flounder fillets on individual plates or a serving platter. Spoon the warm lemon butter parsley sauce generously over the top of the fish.

11. Serve immediately with lemon wedges on the side and your favorite accompaniments, such as steamed or sautéed green beans, roasted potatoes, or a simple green salad.