Olio's Mezzaluna   (Photo: Boru O'Brien O'Connell/New York Magazine)

Pizza aficionados might have noticed something unusual at one of the city’s newest authentic Neapolitan pizzerias. Amid the Margheritas and the marinaras at Olio Pizza e Più (3 Greenwich Ave., nr. Sixth Ave.; 212-243-6546), there’s something called the Mezzaluna, a bizarre but tasty pizza-calzone hybrid, the pizza section topped with smoked mozzarella and cherry tomatoes and the puffy calzone edge stuffed with ricotta and sweet soppressata. “I don’t like to be static,” says Olio’s master pizzaiolo Giulio Adriani, who claims to have invented the thing on a whim one night at his Roman flagship in 1997. But as it happens, New York already had its own homegrown Mezzaluna. A couple of years ago, recounts Joe Mancino, owner of Peppino’s, in Brooklyn, “a guy came in and he didn’t know what he wanted, a pizza or a calzone. So I said, ‘Let me try something.’ ” He named the asymmetrical result the Pizza I Dunno (“What do you call it?” “I dunno”), and sells about 100 a week between his Bay Ridge and Park Slope branches. Necessity may be the mother of invention, but a little customer indecision never hurts.

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