Yes. In fact, the traditional recipe does not even include Parmigiano Reggiano.
Eggplant parmigiana, or eggplant parmesan as we know it here in America, is a bit different from its traditional preparation which hails from southern Italy. So why isn’t it called eggplant Siciliana or eggplant Calabrese? Well, the original name was eggplant parmiciana, not parmigiana. Parmiciana is a word of Sicilian dialect that means strips of wood used to make window shutters. In the original preparation, sliced eggplant is layered on top of each other in the same fashion.
So, how does the original preparation differ? In addition to not including Parmigiano Reggiano, there are no bread crumbs, as is often seen in modern interpretations. Only soft cheeses are used, like mozzarella or tuma, a tangy ewes-milk cheese from Sicily.
Here is another of the great debates among Italian Americans: to salt or not to salt eggplant before cooking. I am referring to a process of sprinkling coarse salt on sliced eggplant and letting it sit in a colander for up to an hour. There are a couple of reasons for doing this. First, it draws out the bitter flavor that is inherent in eggplant. This is really more applicable to bigger eggplant; the baby variety is much less bitter. Second, is to draw out a lot of the liquid so the eggplant isn’t soggy after cooking. Many will argue that this process is unnecessary, and that there is very little difference afterwards.
Here is a great Los Angeles Times article that attempts to settle the debate with an experiment with eggplants that have been both salted and unsalted in a number of popular preparations. The findings? Other than a smoother texture when frying, there really isn’t a large difference in flavor by salting. Now we know.