My first thoughts would be cavalry charges and possibly trying to outshoot them with Genoese crossbowmen - or some combination thereof. Your crossbowmen fire relatively slowly but should do more damage when they do (being high attack and armour piercing plus having good armour and a shield themselves). Terrain could be key there, let them march to you ideally as the AI is often willing to do that.
If you've got gunpowder yet then smashing their morale with that combined with cavalry charges might work.
If you're inside a settlement then it's harder really I'd say, especially as some of their archers are rather good at melee and your chaps would have a hard time firing out from the walls once the enemy is close.
I haven't fought the mongols in a long while so am just giving vague thoughts. If you upload your save file somewhere I'll add looking at it to my rather long 'to do' list