I have seen in case of fundido on some menus but not recently. I ordered it one time at a real Mexican restaurant where I had a language barrier and when they brought it out it was a cup of hard unmelted Monterey Jack cheese or some other white cheese and they had no idea I guess what to do with it and I couldn't even tell anyone about it because everyone pretended nothing was wrong.
So I guess that experience made me think twice before ordering fundido again. Not everyone flambees that same mixture but they melted I guess under a broiler or something and I'm honestly not tried that but it's probably fine. The places I get it they call it by what's in it so they call it hongos con queso for the one with vegetables and poblanos. And then they call the chorizo one something else. But the first couple of places I had it did call it queso flameado and it did not have much in it except cheese and rot gut. But it was good. It's hard to mess up melted cheese and yet I've had it happen to me twice.
If I had the proper pan for it and better insurance, I would be tempted to try it at home. Because I would char and peel the poblanos first and get a good brown on the mushrooms and I think mine would taste better. I think you could use one of those iron steak pans that has the wood casing around it if you didn't burn yourself trying to move it out of the oven and back onto the wood.