It seams that all-cavalry army is the best to beat the Mongols.

I've just had a battle against a full stack timurid army near Constantinople. My army was composed of 3 merc horse archers, 1 elephant artillery , 1 elephant gunners and the rest were heavy cavalry (english knights and knights hospitaller). The timurids had a usual mix of cavalry, horse archers, infantry and elephants, including 2 generals.

I decided to ignore their HA for the moment, and executed a full scale cavalry charge on their center. The result was astonishing, the first cavalry wave completely broke their infantry and archers.

Then I sent my HA after their elephants, they were soon running amok.

While my cavalry were finishing what was left on the center, I decided to deal with their horse archers, only to find they were fleeing from the battlefield.

It wasn't a decisive victory, most of their HA and generals survived, but my casualties were very small.

While the Mongols are still a horde, it's very helpful to have a general with the Night attacker trait, so you can pick them one at the time, rather than face a multiple stacks.