There are a couple actual Mongolian restaurants around here that we visit, as there's a fairly large Mongolian population in the Chicago area. They think I'm neat because there aren't a lot of white dudes that speak Mongolian.I would hope Chicago would have a vibrant community, there are several genuine Mongolian restaurants not too far from my abode here in Central Texas that are quite good. I regret that Mongolia was a part of the World I was not able to see when touring due to politics I would have loved to have experienced the people, food, music and culture.
If you're even in a real Mongolian restaurant I would recommend, in order of my preference,
1) хуушуур (huushuur or khuushuur)
2) цуйван (tsuivan)
3) бууз (buuz)
They're the dishes Americans tend to like the most. I generally like Mongolian food better in America because it's typically made with better meat and more spices.