Challenge: With a POD after 500 AD, have the population of Anatolia become Buddhist.
Okay, how about this? The Huns invaded all of the middle east, India and Europe in the 400s. Kavadh, the persian ruler, actually took their help in regaining his throne. IOTL, they simply were absorbed into the Zoroastrianism, and Hinduism in the middle east. Now, suppose that the Huns convert to Buddhism in the early 500s (both Buddhism and Huns still retained a lot of vitality in the late 400s, and early 500s, and in fact, Huns converting to Buddhism might just be what Buddhism needs to remain influential in both India and the Middle East). All you need for this to happen is a couple of influential preachers, who manage to get the ear of the Hunnic chiefs. The Hunnic chiefs remain allied with the Persians during the reigns of Kavadh and Khusro Anushirvan, maybe ruling a piece of Central Asia. In the aftermath of the Justinian era, they invade Anatolia in conjunction with the Persians as IOTL, except the Persians are more successful, and manage to beat off Heraclius' counter attacks. The Huns end up settling in Anatolia since it is much more attractive than their native Central Asia, and since they are Buddhist, they begin proselytising. In a few centuries, under Hunnic-Persian tutelage, the entire area becomes Buddhist, at least until the coming of the Turks (who might also be Buddhist ITTL).