I've read that there is a very small Mongolian population in Yunnan and that part of that group is here in Kunming (or somewhere nearby). Does anyone know of any Mongolian restaurants in the area?

Any Mongolian food will probably be Kunminized, the way Western food, Japanese and Thai food is here. Don't get your hopes up. In fact people here can't seem to get Cantonese food right even. They resist, or are unable, to mimic food from other parts of China. Best of luck.