Sophia loren's parmigiana

This is a truly magnificent dish, and at the same time an unfathomable mystery to me. Why Parmigiana if this is a dish that is not only as Neapolitan as San Gennaro, but one of the proudest monuments of Naples cuisine? Historical injustice? Involuntary error? Or a conspiracy? In any case here is what it is made of:
Clean and slice some large aubergines, say 2 pounds for 6 people. Each slice should be a little less than a quarter inch thick. Place slices on a large plate, cover with course salt, then cover with another plate and weigh it down with something heavy, so that the slices extrude their bitter juices. After a couple of hours, wash and dry the slices and squeeze them a little, very gently, to get them as dry as possible. Then fry them in plenty of hot olive oil.
Make a sauce with tomatoes (say, under 2 pounds, or slightly less than the weight of the aubergine), peel chop and sieve them; put them in the pan with a pinch of salt and a few basil leaves, but without oil; you only have to wait for a little of the tomato juice to reduce before the sauce starts to thicken. At this point, you put a few spoonfuls of the sauce into an oiled baking dish, then a layer of fried aubergine, then sprinkle with grated Parmesan, then put down a layer of thinly sliced Mozzarella with a few leaves of basil, and a spoonful of beaten egg. Begin all over again with the sauce, the aubergine, the Parmesan, mozzarella, egg, and back to home base, so that you end up with at least three layers of everything. Bake uncovered in a hot oven (425F) for 40 to 50 minutes.
Variations on this dish, which is revered throughout the length and breadth of Italy, included one with the aubergine dipped in egg and flour before frying, so that the taste is more delicate. It can also be made with half aubergine and half courgette, which is more delicate still.