Russia’s great expanse stretches south from the Arctic for many thousands of miles until it comes to a halt at the long spine of the Greater Caucasus Mountains. The republics on the northern side of the Caucasus, including turbulent Dagestan and Chechnya, still belong to Russia. Azerbaijan, Georgia, and Armenia, on the southern side of the mountains, gained their independence when the Soviet Union collapsed in the early 1990s. The high slopes are home to shepherds and the descendants of clans who have long lived there. Lower down, where sleepy towns look up from valleys to the snowy peaks, bigger communities try to scratch out a living.

In one of these towns—Oguz, Azerbaijan, a four-and-a-half-hour drive from Baku, the country’s oil-booming capital on the western shore of the Caspian Sea—live up to 80 Mountain Jews among a population of more than 6,000. The history of the Mountain Jews, who live mainly in Azerbaijan and the Russian republic of Dagestan is, according to members of the community, rooted about 2,500 years ago in their exodus from Israel, their gradual passage through Persia (where they picked up the Farsi-based language they still speak), and their eventual settlement in the Caucasus mountains.

Sitting in the dark-stone building that houses Baku’s Mountain Jewish synagogue, Semyon Ikhilov, the Mountain Jews’ national leader, shakes off the idea that his people might be descended from indigenous Caucasian mountain dwellers who converted to Judaism. “We’re real Jews who came out of Israel,” Ikhilov said, explaining that they acquired the moniker “Mountain Jews” because they settled in the peaks. “We were not mountain people.” And according to a recent genetic study led by researchers in Israel and Estonia, Mountain Jews share a common origin in the Levantine region of the Near East with other Diaspora Jewish communities....