• Chris Wickham, The Inheritance of Rome: Illuminating the Dark Ages, looks at the early medieval history of the regions that were once the Roman Empire. So although it's not the whole world, it does cover the Islamic world and Byzantium as well as the more traditional Western Europe approach.

• Peter Brown, The Rise of Western Christendom, obviously focuses on western Europe and religion/the Church (in spiritual and political terms), but is wonderfully readable and often used as a textbook in early medieval history classes

• Amira Bennison, The Great Caliphs: The Golden Age of the Abbasid Empire, a.k.a. "The only thing 'dark' about the medieval Islamic world was the night sky"

There are a few others that are "general reader"-friendly overviews, but those are my go-to recommendations. :)

In addition to what /u/sunagainstgold mentioned, don't forget to check out the sub's book recommendations on the Middle Ages.