As Egypt on Vanilla 1.2 H/VH settings, i found the best way to deal with them is to send out some mamluk archers and do what you can to get around behind them and destroy those blasted trebuchets and rocket launchers. After that, its easy since they are easily defended against in sieges and good defensive battles (not necessarily bridge, a good hill battle works just as well if you have enough spears to hold your lines against their cavalry, while your archers pick off theirs). Strangely enough, they appeared near Tblisli and Baghdad but every wave wanted to come take over my new capital, Jerusalem. Even though they had 4 full stacks sieging me, i found it quite easy to disperse them defending if you actually let them on the walls, and break up any units they try to ram the gates down with. Just manage your archers away from ladders, and have them shoot the mongols up as they come over the wall. It's hilarious watching many hundreds of infantry die to archers direct firing them on the wall