Do keep in mind that the Carlin podcast is not history so much as it is entertainment. He himself says he's not a historian but a fan of history. You should take what you've learned from it with a grain of salt.

That said, we have a number of books on Mongolia that have been recommended by our flaired users. They are as follows (descriptions included):

Genghis Khan and the Making of the Modern World by Jack Weatherford: An nice introduction, entertaining, interesting and good for history geeks and the general population. However there are some misrepresentations that the author makes, so follow it up by reading some criticism to see what he got wrong e.g. bad translation. However the main issue is in placing so much emphasis on the positive aspects of the Mongols, partly as a counter to their usual bad press, the reader risks coming away with a somewhat distorted impression of the Mongol Empire.

The Mongols by David Morgan: Absolutely standard text in the field. Gives an excellent grounding in the history of the Mongol Empire, although it is strongest when discussing Ilkhanate (A Mongol successor state based around Iran). Ideally read the second edition, his views evolved substantially between the first and second publication, he explains how and why his views have changed on the Mongol administration.

Genghis Khan and Mongol Rule by George Lane: This book examines the entire Mongol Empire but its real strength lies in its examination the Ilkhanate, especially the early period. It's best read after David Morgan's book as much of that work is a direct challenge to Morgan's theories, so it's good to know what he's challenging. Amusingly this guy was David Morgan's student, and his book is heavily based on the PHD he submitted to him.

Culture and Conquest in Mongol Eurasia by Thomas T. Allsen: Be warned this book is very dry, mainly of interest to someone who already knows a fair amount about the Mongols. It basically takes an in depth look at the the exchange of goods, ideas and people between Yuan China and the Ilkhanate (based in Iran), two states ruled by Mongol dynasties descended from Genghis Khan. It's fantastically detailed, or horrifically detailed depending on perspective, and provides an unparalleled examination of exactly what was and wasn't transferred by the Mongols, the agency by which things were transferred and how much influence these new ideas, goods, etc, had.

The Mongol Conquests in World History by Timothy May: Another excellent introductory text, more detailed than Morgan. Also provides the best clarification of the unholy mess that is terminology in early Mongol government. If that makes it seem dry let me assure you the book isn't, it very readable and very well informed.

Hope that helps.