If you're curious about classical Iranian music, I highly recommend looking up Kayhon Kalhor. He is an extremely talented Kurdish musician (mainly playing the kamancheh, which is a sort of proto-violin) who often collaborates with Yo-Yo Ma. I particularly like Ascending Bird, in collaboration with the Brooklyn Rider. His duet performance of Morghe Sahar with Yo-Yo Ma is amazing too.

Hayedeh, Mohammad Shajarian and, more recently, his son Homayoun Shajarian are also amazing singers. Chera Rafti is very popular introduction to Homayoun.