What is the best-known book set in Azerbaijan?

See note on methodology

There is no competition here. Azerbaijan is at the edge of Europe, and there is one great (and fairly short) novel set there (with excusions to Dagestan and Iran) before, during and after the first world war, chronicling the love of an Azeri boy for a Georgian girl, and how it all concludes in British betrayal. (Be honest, did you know that the British had betrayed the first democratic and secular republic in the Muslim world back in 1919? You do now.) First published in German in 1937, by an author whose identity seems peculiarly elusive (though I am convinced by the argument that he was a Jewish convert to Islam, who wrote mainly in Berlin but died in Italy), it is:

Ali and Nino / Ali und Nino by "Kurban Said" (likely Lev Nussimbaum)

Only two other books really place here, and neither is wholly satisfactory on the geographical criterion. One is the biography of that Jewish convert to Islam, whose mother took tea with the young Stalin and whose grave became the punchline of a comic story by John Steinbeck, who probably wrote the previous book – obviously a major piece of detective work in itself, but at the same time largely set outside Azerbaijan as it chronicles the geographical (and other) wanderings of its subject and author. It's also a jolly good read, and I recommend it. It is:

The Orientalist: Solving the Mystery of a Strange and Dangerous Life, by Tom Reiss

The other book that places well, with far more owners than the first two on both LT and GR, but with the crucial disadvantage that it is mostly set in tenth century "Khazaria", which I believe does not overlap very much with Azerbaijan, though it's fairly clear that the opening chapters are indeed set in what is generally recognised as Azerbaijani territory today. First published in 2007, it is:

Gentlemen of the Road, by Michael Chabon