I highly recommend:

1. Destiny Disrupted, by Tamim Ansary. It’s an extremely broad, sweeping history of what he calls the “Middle World” between Europe and east Asia and a concise history of Islam. You probably already know a lot of what it covers, but he’s such a fantastic writer that I couldn’t put it down.
2. The Lost Enlightenment, by S. Frederick Starr. It’s a history of Central Asia mostly during the Abbasid Caliphate. This was a real eye-opener for me — I knew that Baghdad was a major center of civilization during the Middle Ages but I didn’t realize just how much that came from Persia and Central Asia.