Well,

My best battle.

Mongol Horde vs Byzantines(me)
Troops: 2500 Mongols vs. 3000 Byzantines
Volga Bulgaria

This battle took me bout half an hour to make, and both os us attacked only with cavalry charges. I only had 2 units of Kataphraktoi, which saved the day. The Emperor and 1 other unit. I had tons of Pronoiai Allagion and Armenian Heavy Cavalry(my game is modded). Wave after wave of cavalry, until I was forced to regroup and rest my troops, because all of my unit were very tired or exhausted(the Emperor was Totally Exhausted) . Reinforcements came in, as I rested my troops. 400 Byzantine Infantry. Reinforcements for them also, consisting of Mongol Heavy Cav, Mongol Warriors, Mongol Horsa Archers and Steppe Cavalry.
On my final charge, as I made the Cavalry Formation, and crushed the Mongols after some hard battles. Their Khan was killed, and my Emperor got +5 valour.