Pin and flank.

Let some spears take the inevitable charge, and send something with a good attack (even if it has bad defence) to hit them in the sides or in the back if you can.

Militia sergeants might be your best Katank-flanking unit, or maybe Italian infantry can be the attack as well as defence. Pin with one on hold position/formation, and charge in another on engage at will - Italian infantry can do everything.
Mounted sergeants might also work, but you should repeatedly charge and pull back.

Try a ballista. It can't stop the whole unit, but if you can kill the leader with it, then you don't have to fight a jedi, and Katank leaders are always uber-generals with 6 stars, killer instinct virtues, etc, so killing them really decreases the effectiveness of the unit.
(Not to mention routing all the peasants, vanilla spearmen and slav warriors that the Byz fill their armies with for some reason).

Dismounted CKs can walk into the front of charging Katanks and shred them, but I guess we're talking about the early period here.

One more thing: check your inns. You might find something useful which you can't build yourself - mounted XBows (oddly available in Early even though the 2-legged version is not ), vikings, javelins, or maybe even camels.