To fillet, insert the blade of a sharp knife on one side behind the head and cut in an arc down to the bone. Then score the flesh along the sides and across the tail. Finally, insert the knife behind the head and slip the knife along rib cage, cutting the fillet away from the ribs. A large flatfish produces two fillets on each side. To skin the fillet, place it skin-side down on a board. Starting from the tail, slide a sharp knife between the skin and the flesh.
The secret to successful flounder cookery is to not overcook. Whichever of the following cooking methods you choose, your flounder will be cooked when its flesh becomes opaque but is still moist and is easily pierced with a fork.
Place flounder in a greased baking dish, or wrap in oiled foil and place on a baking sheet. Brush the fish with melted butter or oil and season with salt and pepper, or cover with a piquant sauce. Bake in a preheated 450°F (230°C) oven until done, about ten minutes for each inch of thickness.
Rinse flounder fillets and pat dry with a paper towel. Place fish on a rack above a baking dish. Preheat the broiler and adjust oven rack so fish is 3 to 4 inches (7.6 to 10cm) from the element. Broil, turning once, until fish is opaque but still moist in the center, about three to ten minutes, depending on size of the fish.
Coat flounder with seasoned flour, crumbs, or cornmeal. Shake off any extra coating and fry in a small amount of hot butter or oil, turning once halfway through cooking time. Cook until fish is opaque and moist on the inside, about four to eight minutes.
Pour oil into a wok or deep fryer; it should be at least 1 1/2 inches deep, and the cooker should be less than half full of oil. Heat oil to 375° F (190°C), using a thermometer to monitor temperature. Cut boneless strips into similar-sized pieces about 1 1/4 to 1 1/2-inch (3 to 3.8cm) thick. Dip in batter, drain, and then slip pieces into hot oil. Cook until brown, about two to three minutes.
Bring poaching liquid, consisting of water, broth, herbs, and spices, to a simmer. Slip in the flounder, then cover the pan and keep the liquid at a simmer for about eight minutes per inch (2.5cm) of thickness.