Someone was looking for chicken parmigiana recently on this board, and while this probably isn't exactly what you had in mind, I was at Buon Italia in Chelsea Market yesterday and had an excellent chicken cutlet sandwich. The one I had was a really fresh breaded chicken cutlet with cooked greens, but they also had cutlets with tomato sauce and grated cheese and a slice of eggplant that looked equally good. It's probably not the messy sub/hero experience you're looking for (the sandwiches aren't huge), but I bet it tastes good. Actually, I've liked all the sandwiches I've tried there. The meatball sandwich is great, and yesterday I had a great prosciutto-mozzarella-arugula combination (with maybe a little stracchino spread on there?) on a flat, round roll. Sunday seems to be sandwich day: They were bringing out big trays while I was standing there (around 1:00), so everything was particularly fresh.
Everything is a little more expensive than it should be there (except for the pizza, which is also good--I prefer the kind without cheese, just tomato), but I never regret it.
Oh, and Francesco made me an espresso afterwards, and I think his is the only good espresso in Manhattan.