New York has never had a shortage of old-school red-sauce spots or exuberantly expensive odes to Italian cooking, but the last few months have seen a serious uptick in restaurants and cafés from Italians eager to introduce New Yorkers to the way Italy eats now, whether that’s sandwiches served on the Florentine answer to focaccia, strong cocktails poured in a bar bedecked in dark wood and Carrara marble, or regional cooking from Piedmont, Tuscany, and Emilia-Romagna. Here are the new molto Italian restaurants that demand your immediate attention.