Fact is, no one knows—which only goes to show how uninteresting facts really are. At best, if well chosen, they’ll point out what needs explaining, but they rarely explain it. They may speak for themselves, as the saying goes, but they don’t have much to say about anything else. Mostly they just assert themselves, as things needing to be explained.
So I start working up a diatribe against the pretensions of the Parmesans, about how the true origin of a thing should be credited to its final perfecter rather than its first confecter; that it is not its factual birth that reveals its true nature, but its full flowering; that, whatever inchoate beginnings this eggplant dish may have had among the Parmesans, its true form was clearly achieved in South Italy and disseminated thence throughout the Americas by its emigres …. You get the idea.
I brine my eggplant slices (i.e., soak the slices in water as salty as the sea—¼ cup salt to 1 qt. water—using a plate to keep them under water) for as little as ½ hour or as much as a couple of hours. I believe without proof of the fact that this brining leeches out any bitterness and also renders the slices less absorbent of oil during frying, by hydrating them. I repeat, I have no proof of the fact, only this theory why. [It appears you can have a reason why without a proven fact to go with it.] When I’m ready to fry them, I dry them off by spinning them in a salad spinner, in small batches. Sometimes I rinse them with fresh water before draining and spinning them dry.
It's when it comes to frying the eggplant slices that the two recipes first diverge. For Marcella's eggplant parmigiana alla Parmesana (which name we now understand is not in fact redundant), I very quickly fry the eggplant slices plain (no flour, breadcrumbs, or egg), in nearly an inch of maximally hot peanut oil, until the bottom edges are gilded, which usually happens in under a minute, whereupon I turn them over to reveal their happily golden, bespeckled faces, and go on to gild the other side as well, in well under a minute (even as little as half a minute, if my oil is maximally hot). I remove the slices to racks to cool (or else paper towels), and taste to see if they need salting on both sides, which they usually do.
Anyway, to do it my mother's Brooklyn way, beat a couple of eggs in a flat bowl with a pinch of salt and dollop of milk. Then pour out seasoned breadcrumbs—preferably the 4C Seasoned Bread Crumbs—in a big mound onto a paper towel, together with some tablespoons of flour, using the corners of the paper towel to mix the flour into the breadcrumbs. Dip an eggplant slice into the egg to wet both sides, let excess run off, and then place it on the mound of crumbs, using the towel corners to cover the top of the slice with crumbs; press the slice into the crumbs below; then turn it over, top again with crumbs, press again. Set breaded slices aside in a single layer on a tray or paper towels, to dry off.
But I digress. I'm supposed to be slicing mozzarella for my mom's breaded eggplant sandwiches. I slice the mozzarella into slices a bit less than half the thickness of the eggplant slices, and sandwich the slices between the eggplant slices, to cover without overhang. Also tuck in several big crumbs of Pecorino Romano, which you can produce by fork-whittling your grating chunk. Spread a little sauce all over the bottom of the baking pan, and lay out the sandwiches. Then top each sandwich with a generous spoonful of sauce, but not running over. Spinkle the mounds of sauce generously with grated Pecorino Romano. Bake in a moderate oven, say 325-350 degrees, until the mozzarella has melted and starts to ooze out, say 20-30 minutes. My mother covers the baking pan very lightly with aluminum foil, which she removes in the last 5-10 minutes, but I find the foil unnecessary.
P.S. Do I ever make a sandwich with it? No. The happy proportion to bread is achieved by eating the eggplant with a fork in one hand and a piece of bread in the other.
P.P.S. Do I need to tell you to take bites of the bread in between?
* Lay the sandwiches out in a broad and well-buttered pan, and top each sandwich first with a mound of grated Parmigiano-Reggiano cheese and then a few big curls of butter.