Over the holidays we drove from Saskatchewan to Columbus, Ohio for a wedding. We spent Christmas in Chicago and got to enjoy wet hot Italian beef sandwiches. Wow, they were great! A big thanks to my wife who found the place, Al's #1Beef.
The meat is basically slow cooked in a vat of fat, meat drippings, and broth. A wet Italian Beef is when you dip the bread of the sandwich fully into that vat, then pile the meat on top.
I make roast beef all the time with carrots, onions, potatoes and mushrooms. Never once had the thought of adding it to a roll. Chicago's food is something else.
You can order it dipped, wet, or dry. Wet is the traditional so it usually just has one or two ladles of juice poured over it. Dipped is when they dunk the whole thing. But the bread is high quality so it can usually take it. I prefer wet myself (hehe).