Except for authentic Dover sole, from the European side of the Atlantic, flatfish fillets are fragile once cooked. Since their skin isn’t very savory, it is best to remove it. Because they are thin, there is no point in trying to brown them using high heat. They will cook through in a minute. Instead, cook them in butter in a nonstick pan over medium heat. They can also be dusted with flour or coated with flour, beaten egg, and fresh bread crumbs (the same way as the