Mongols, in the historical sense, did not have an agrarian culture. However, what is currently eaten is not a solid indicator of what was eaten in the pre-modern period of Mongolian history. Most of their food came from the flocks, whether sheep/goats, horse, or cow. What little agriculture they preformed, was usually what they would find in the wild. Wheat generally was, as you'd know, a wild crop which was domesticated. The Mongols would find wild wheat and then plant it near either their winter or summer pastures. By the time they came from one pasture to another, they would have wild wheat and they could use it. Wild Onions were another staple which they would use.

Other items, such as more wheat or rice were generally traded with either the Chinese or other settled people for items which the agrarian people could not produce themselves. Most of the conflict between the agrarian population and the nomadic population, in terms of Mongols, was due in part to the restrictions that China would place on trade. The Chinese would often dictate where and when they could trade and how much each thing was worth. Disagreements often flared up resulting in the nomadic tribes, including the Mongols, forcing China to open up for more trade.

For more on this I suggest reading these sources:

• The Perilous Frontier: Nomadic Empires and China, 221 BC to AD 1757 by Thomas J. Barfield
• Peace, War, and Trade Along the Great Wall: Nomadic-Chinese Interaction through Two Millennia by Sechin Jagchid and Van Jay Symon
• Mongolia's Culture and Society by Sechin Jagchid and Paul Hyer