Does the PoD have to be in the Ottoman wars?
How about going a little bit more back: Mongol invasions. Have the Hungarians be more successful early on, settle the Cumans and have the king successfully bring the nobility in line by the time the Mongols arrive, so you have a better led, better prepared and larger Hungarian force present at Mohi. Have them win a very decisive victory. Reading on the battle, I think it's absolutely possible, since it was a river crossing which did not favor the Mongols. Just have a larger light cavalry contingent (the Cumans) who will screen the Mongol right wing trying to ford the river and have the king actually be prepared to leave camp in time so the bulk of the Hungarian force can engage the Mongols while they are forcing the river crossing (OTL the Hungarians had only a small vanguard there while the main force was in camp, not even in armor). The battle has to be so disastrous that the Mongols have to retreat to Halich to regroup. This would give time to fortify the mountain passes, so only small raiding forces and not large armies could cross. Remember, the Hungarians only have to hold out for two years, before Ogedei dies and the Mongol have to return for Kurultai. Maybe even better: have Batu Khan injured in the battle by a crossbow bolt and die shortly after the battle. Maybe this creates enough confusion for the Mongol force to entertain themselves until Ogedei finally dies.
That, or just have Ogedei die two years early. But that would have enormous butterflies all over Eastern Europe.