It's the historical conundrum that sedentary armies faced against the many steppe armies that terrorised Europe.

As for counter units and Cantabrian circle ... Again a historical problem and wrecklessly pursuing HA with cav had disasterous consequences. On the other hand, without Cantabrian circle, archers are a match for HA, which is why the HA must employ this method of attack. I would attempt a wide flank with cav and then try to trap them between these flanking units and a direct cav attack from the main line. Not easy admitted, but it should not be easy. If there was a straightforward counter unit the HA factions would be as weak as the Golden Horde was in MTW

.......Orda