Viktor Bout

Boris Korkin still remembers the three-liter jars of a fizzy, tart drink that would sit on the windowsills of the crowded, five-room communal apartment in central Moscow where he grew up with his mother after World War II.

The concoction was made from an odd-looking blob of bacteria and yeast referred to in Russian as a chayniy grib, or “tea mushroom” — which is also the name given to the beverage itself. When bottled with sugar and tea and left to sit for a week, the solution would ferment to produce the very slightly alcoholic drink he guzzled as a child.

“We drank it because it was all we knew. It’s what we had, and everyone had it,” Korkin, 72, said. “On special...