Cowards!! Take them in the open. No cowering behind walls and bridges. Shame on you, you sound like the French!

The main mongol tactic is shoot you up to soften you, then charge and watch you rout. It works pretty well.

Take 3 or 4 good stacks. Make sure each is commanded by a general with night fighter. Take lots of archers - to win the initial duel and see off the HA. Lots of good spearmen - to stop the charge. And several high chiv generals (high dread doesn't help your own morale. With the mongol xp they aren't fragile so the best bet is boosting your own).

Now try and pick off the edges of his convoy. 2 -1 if possible. You can win inthe open and it's more fun - but you will lose a lot of units. Lots and lots. But as said above if you can take out 1 general it's a huge moral victory - captains have no night fighting and they won't retrain so the armies get weaker and weaker.

It's attrition and it's not pretty. But it is possible - I had much fun doing this with scots pikes and noble archers backed by generals. It was even easier as turks, I abandoned my HA armies that I had previously used and switched to janissary archers (for stakes) and ottoman (for good stats). Inf used dismounted sipahis and saracen militia (the jhi crumble under charges). Genrals and qapakulu for horsies.

remember: You have an empire and can replace losses. He just gets weaker and weaker. If you face the dreaded Mongol Shuffle while waiting at choke points and walls it will be very, very boring.