A couple things that come to mind, from a definite non-Asianist:

We recently hosted an AMA with Jack Weatherford, who has written extensively on the Mongols!

There is also Barbara Demick's Nothing to Envy: Ordinary Lives in North Korea, which looks at the 1990s in particular and is utterly engrossing.

William Dalrymple writes excellent popular history about South Asia, specifically with regard to the Muslim states of North India.

The Last Mughal (on the 1857 Indian Rebellion) is excellent, as is City of Djinns (a history of Delhi).