"not really authentic" does not even begin to describe Fire & Ice. The whole concept of these "Mongolian BBQ" restaurants, which includes the ubiquitous "Mongolian Beef" dishes at Chinese restaurants, has nothing to do with Mongolia at all. What we have today is some complicated combination of post-Meiji restoration Japanese steakhouses, which were brought to Taiwan during Japan's colonial occupation of the island, and found a kind of re-branding as "Mongolian" in Taiwan post WWII. I think Mongolian beef found its way onto the menus of American Chinese restaurants via Taiwanese immigrants, and mingled with the Japanese tepanyaki restaurants (i.e. Benihana) to produce monstrosities like Fire & Ice.
Now, if you mean food like that which is currently eaten in Mongolia, you do have a few options, in a very limited sense. There's Silk Road BBQ, which has a stall near the Financial District for lunch and possibly other locations. I've had their grilled lamb skewer, which they say is flavored with Uzbek spices. Personally, I didn't think it was anything special.
Some Chinese restaurants in the area have lamb skewers with the flavors of West China. I've been to the Chinese province of Inner Mongolia and had similar tasting food there, but I've never been to Mongolia the country. The best such lamb skewers are at Gene's Chinese Flatbread Cafe in Chemlsford. One of the Kind in the Super 88/Hong Kong Market food court in Allston, and Golden Garden in Belmont, also have good BBQ lamb skewers. Many authentic Chinese restaurants, including Golden Garden, as well as Zoe's and Wang's in Somerville, have a dish called Cumin Lamb, usually served in a bed of cilantro.
Finally, you may find that the Afghan dishes at The Helmand in Cambridge or Ariana in Allston are something like Mongolian food. Jibek Jolu in Chicago IL is a terrific Central Asian restaurant that I've enjoyed --- there is some overlap between those Afghan menus and Jibek Jolu's.
There are extremely few Mongolian restaurants in the United States, like Asian Grill in Oakland CA and Teriyaki Joy in Seattle WA. Both offer other kinds of cuisine, but are owned by Mongolian owners and have a Mongolian section of their menus. You can get an idea of what is on their menus here:
There are also some Mongolian restaurants in Beijing, but I have never been.
Wow! What an awesome response to my question. I never knew the Taiwanese connection to the Mongolian BBQ joints, but that totally makes sense. My only experience with Mongolian BBQ comes from a spot in Washington DC which is housed under (and owned by) a Chinese Restaurant.
I will definitely bookmark some of the spots you've mentioned! The Helmand is a favorite of mine and I always order the lamb there.
Thanks again for your response! Greatly appreciated.