You never know what you’re gonna get. At Surprise Scoop, a new ice cream shop in the East Village, customers don’t get to choose a flavor. The only menu item is “surprise ice cream” ($9.18).

At his new ice cream shop, Jesse Pruchnik serves cones, shakes and sundaes with a beaming smile. “What can I get for you today?” he asked Xavier Stauder, 6, on a recent evening. The little boy ...