Heat oven to 375° F.
With sharp knife, cut the top and bottom of both eggplants. Then slice in half, vertically. Holding one half of the eggplant upright, - carefully cut thin vertical slices, about 1/4 inch thick.
Salt both sides of the eggplant slices and lay flat on a cookie sheet lined with paper towels. Cover with another layer of paper towels and then lay something heavy on top (like a rectangular casserole dish) and let sit for one hour. This helps to extract some of the water.Note: This step can be skipped, but I do find it removes some of the bitter taste and helps the eggplant to absorb less oil when frying. For breaded slices, dip both sides of eggplant slices in flour, then dip in egg mixture, and then fully coat in bread crumbs. Brown each side and place on paper towel. Repeat steps until remaining slices are cooked. For the non-breaded version:Heat fry pan to medium; add olive oil to cover the bottom. Once hot, carefully add a few eggplant slices at a time (don't overlap) and fry until medium-golden brown (just a couple minutes). Turn over and do the same on the other side. Remove the eggplant and lay flat on a paper towel. Repeat until one of the eggplants (or half of the eggplant slices) is fried. Note: The slices cook fast, and they absorb a lot of olive oil. This is to be expected. In 9 1/2-inch baking dish, add marinara sauce to lightly cover the bottom. Add a layer of eggplant, and then sprinkle with grated Pecorino. Add a layer of mozzarella cheese, dollop sauce over the cheese and repeat this layering a few times.
After the third layer add sliced hard-boiled eggs. This step is optional, but I highly recommend it. Continue with alternating layers of eggplant, sauce, cheese, finishing with sauce, cheese and a parsley garnish.
Bake in oven at 375° for about 35 minutes until the top layer of cheese is golden brown and the top is bubbling. Let rest about 10 minutes before serving.