Mongolian beef has been a long-time favorite on Chinese restaurant menus. The dish isn't complicated in its ingredients, but manages to contain an explosion of flavor. Thinly sliced beef is stir-fried in little more than soy sauce, ginger, garlic, a little sweetener such as hoisin, and green onions.
Although it's an excellent contribution to the hungry masses, you're not actually getting a taste of Mongolia at all when you order it. Mongolian beef was most likely created in Taiwan by Chinese immigrants to the country in the middle part of the 20th century. Even stir-frying, the method of cooking the dish, is Chinese in origin.
At the same time, Chinese and Taiwanese cuisine was becoming popular in the United States due to the number of immigrants coming west and opening restaurant businesses. Americans would have been attracted to a dish like Mongolian beef because the ingredients were familiar to them but it still offered a taste of exotic cooking. It may have been labeled as "Mongolian" as opposed to "Chinese" or "Taiwanese" simply for marketing purposes as Mongolia was generally more of a mysterious locale than the latter two countries.
In reality, there is really nothing inherently Mongolian about Mongolian beef, and you sure won't find it in the country it's named after. But you will find several excellent dishes using ingredients that you might not be so accustomed to. So, if it's exotic cuisine you're looking for, consider visiting.
Beef is actually rare in authentic M.