There are more than a few foods in Turkey that sound strange to outsiders: chicken breast pudding, lamb's intestines, sheep's head sandwiches (more on that in a future post!). I'd definitely put the fermented grain drink boza in that category.
Different grains can be used, but here at Vefa Boza, it's millet that's ground and then fermented. The resulting drink is very thick and just a touch alcoholic, with the smooth-but-substantial quality of... I hate to say it, but baby food. Or super-smooth applesauce. And maybe it's just the texture, but the taste had me thinking of a much richer applesauce, too. It's both sweet and sour, and sprinkled with cinnamon (and, in some places, roasted chickpeas. Awesome).
It's so substantial a cup could really serve as a meal replacement. The kind of stuff you'd feed your super-skinny kid to try to put a little weight on him. Easy to see why it's considered a cold-weather drink; in the summer, I'd imagine it's pretty unappealing. "In the winter," Hande Bozdogan of the Istanbul Culinary Institute told me, "you'll see boza vendors on the streets with tanks on their backs, and you bring down your own container to fill it up. You hear them from the street, bellowing bohhh-zaaaaa."
You'll find it bottled and sold all over Istanbul, too, at markets and stores. But like other fermented products (say, kimchi), the sour flavors get more pronounced over time. So your several-day-old boza might be a good bit more tart than when you first buy it.
Worth a visit, if only to see the historic shop itself, which dates back to 1876.