The artichoke may be the quintessential New York vegetable: tough on the outside, with lots of seemingly impenetrable layers obscuring the soft, sweet heart. Years ago, when Sandro Fioriti brought crispy crackling carciofi alla giudea out of the Roman Jewish ghetto and onto the plates of adoring New Yorkers, artichoke lovers rejoiced. (He still serves it at his Chelsea trattoria Sandroís; few do the fried and flattened flower better.) But there have always been warring factions of artichoke eaters: the patient peelers and dippers, for instance, delaying gratification with each increasingly softer leaf, and the stuffing buffs, for whom the plant is nothing more than a sturdy vehicle for oil-soaked, garlic-suffused bread crumbs. We side with chef Jody Williams of Convivium, a romantic Mediterranean haunt in Park Slope. For her traditional carciofi alla romana, she strips a pair of jumbo artichokes to the succulent core, braises them until fleshily tender, and perches them in a pool of olive oil, white wine, garlic, and fresh mint thatíll have you reaching for the basket of crusty brick-oven bread again and again.