AHC/WI: A lasting Mongol presence in Europe

How can the Mongols establish a more lasting presence, territory/ culture-wise, in Europe?

Assume that some Mongols assimilated into European culture (and even convert to Christianity), but managed to retain their own identity, can these Mongols build a nation similar to the Crimean Khanate?
 
I believe they already have through the Golden Horde, at least depending on where you set the boundaries for Europe.
 
I actually want to see a scenario similar to the Turkic people, when they migrated to Anatolia and established a lasting state there later on.
 
The Mongols would of had no interest in anything beyond Russia, they didn't settle in the Rus states because the land wasn't good for their lifestyle.
 
I could see a Mongol horde in Pannonian Plain up to Danubian basin (taking some lands off the IOTL Golden Horde), more or less replacing Hungarians and establishing a Rus-like domination Eastern-Europe (possibly on parts of HRE as well).

While I'd expect a more or less quick "Europeanisation" (trough Christianisation, Mongol-way meaning not that focused on religion), it could significantly alter the ethogenesis in Eastern Europe, especially making Ukranians and Bielorussians more distinct from Russians; or stabilize the situation in Balkans, making Byzantium lasting longer would it be by sheer "protection".

HRE domination over Italy would be certainly much harder, if at all, to maintain (critically with a clearly weakened HRE).

Of course, you'd have huge consequences over Western Europe, probably as much as Ottomans created in their conquest of Eastern Europe IOTL (a good parallel, IMO) : eventually, trough mutual influence, you'd end up with a status quo, while regularily put in question on opportunity strikes.
 
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