Answer:
There were many great empires in the medieval Asia, but among them I would choose Mongolian Empire and Persian (Sassanid) Empire.
Step-by-step explanation:
Mongolian Empire started spreading during the reign of Genghis Khan and later spread across Central and East Asia, and even Europe. It was the largest medieval Empire that we know of.
The other one is Sassanid Empire, that lasted until 651 and was one of the most important empires in Early Middle Ages and also one of the main opponents of the Byzantine Empire.