I don't know if the cookbook includes a recipe for Italian Beef or if it has you pick it up from a place that specializes in it. (She is in Chicago, after all.)
I've made the Jeff Mauro Italian Beef recipe (without the garlic), I thought it was OK but not quite up to Chicago standards.
My son has been making Italian Beef (not sure what recipe he's using), he says the real secret is having an electric slicer that can get uniformly thin slices so they soak up the gravy properly. There was an ex-Chicagoan running a restaurant in downtown Pittsburgh that did a pretty fair Italian Beef (I had it once, I agree.) Before David got his slicer, he was taking his cooked meat downtown to have the guy slice it for him, and the guy said his Italian Beef was pretty good, though I haven't had it yet. The restaurant closed a while back but I think the guy is running a food truck now.
IMHO, the real secret is the right kind of bread, something that won't fall apart when it gets soggy. The Pittsburgh guy was bringing bread in from Chicago, but I think he was making the beef himself.
There's a place in downtown Lincoln that advertises Italian Beef, but IMHO it's just a French Dip, it lacks that Chicago aftertaste. There was a Chicago Hot Dog place at a mall that had Italian Beef that was reasonable, but it closed. They had supply issues, half the time they were out of the beef or the rolls, one time they were out of Vienna hot dogs.
Portillo's is looking to expand (Tony sold out for about 950 $million a few years back, but kept the real estate the restaurants are in), but I don't think Nebraska's on their target list. The WSJ had an article on Portillo's a while back, their AVERAGE location does about $7 million a year, about twice what a typical McDonalds does.
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