From freakshakes to curiouser-and-curiouser flavor experiments, we’re living through an extreme moment in ice cream. So where do we go from here? Back to the past—as in, to the 19th-century Mediterranean. The region's classic ice cream has a surprising texture unlike anything most people, at least in the West, have ever tried. That ice cream is stretchy and chewy—chewing-gum chewy—and it comes from Turkey, Greece and the Levant region of the Mediterranean.