From vinegar-laced barbecue to seafood fresh from the coast, these recipes capture the Tar Heel State’s distinctive flavors.Credit: Food & Wine / Photo by Sara HaasOne of the earliest surviving images of cooking in North Carolina dates to the 1580s. In a delicate watercolor, failed English colonist John White paints intricately scaled blue fish, their bellies fading to white, laid atop a wood lattice propped over an open fire. More fish, slightl…