A more radical POD might be possible 150-200 years earlier. All that has to happen is for an alcoholic's liver to hold out and keep him alive for another year.
Ogadei Khan lives until 1242. As a result, Subotai and Batu Khan carry on the Mongol conquest beyond Hungary. They meet little or no resistance in the Holy Roman Empire because the Holy Roman Emperor's forces are encamped at Rome, so Batu goes to Rome and forces the submission of both the heavily outnumbered forces of Frederick II Babarossa and the Imperial Roman forces (with a hung College of Cardinals). In the meantime, Subotai with over 75,000 troops invades France and catches King Louis XI who is at war with the English King Henry III in what would OTL lead to King Louis's victory in the Saintogne War. The Mongols destroy and annihilate the badly outnumbered French knights, killing Louis Capet ITTL. Henry, who would have had to submit and offer fealty to King Louis anyway OTTL knows when he is hopelessly outmatched and offers fealty to Subotai instead.
At this point, word finally reaches Subotai and his commanders that Ogadei has passed away. The Mongols prepare to withdraw to Karakorum for the Kuriltai. Subotai grants Henry all of France that Louis ruled plus what Henry already rules (basically everything except for Rousillon, Langedoc and Provence, though Henry will get fealty from Langedoc in return for toleration of Catharism from Langedoc's lords). In return, King Henry agrees to send a force of 15,00 knights under Hugh de Lusignan, half of his force, plus whatever French forces survived the Mongols, back with the Mongols to Karakorum detailed to serve under Subotai. Some of them will eventually return to Europe having learned a great deal of the ways of the East including the Mongol ways of war. And his fealty means that he can call upon the Golden Horde as allies, which may serve England in good stead later on, even though the Mongols are withdrawing (temporarily, they say).