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.