Arrange the eggplant slices on several baking sheets and sprinkle generously all over with kosher salt. Set aside to let the moisture bleed out from the eggplant, about 1 hour.
Transfer the eggplant to a colander in the sink, and rinse well under cold running water. Transfer eggplant to a work surface and blot very dry with paper towels. Allow the eggplant to sit at room temperature for about 10 minutes to thoroughly air-dry before proceeding to the next step.
Depending on pan size the actual amount of frying oil will vary, however aim for a 1 inch deep amount of vegetable oil. Frying can begin once the oil reaches 375 degrees. Take your time getting to this temperature as rushing the heating process will result in significantly hotter oil. Once your oil reaches 375 degrees, take a slice of eggplant and dredge it in the za'atar-flour mixture and coat well, shaking off any excess flour before proceeding with the egg dip. Then dunk it in the beaten egg making sure to coat entirely, and lastly coat well in the breadcrumbs. Slowly place the pieces, a few at a time so as not to overcrowded the pan, directly into the oil. Fry for 2-3 minutes until golden, and then carefully flip , cooking for an additional 2-3 minutes until complete. Once finished, transfer the crispy eggplant slices to a plate or baking sheet lined with paper towels to allow the excess oil to drop off. Preheat the oven to 400 degrees. Lightly brush a baking dish large enough to fit all the slices of eggplant, with olive oil. Cover the bottom of the baking dish with 1/3 of the cherry tomato gravy and arrange the eggplant over the sauce. Cover the eggplant with a few tablespoons of the sauce. Place a large slice of mozzarella on each slice of eggplant and top with a healthy amount of shredded parmesan. Repeat with the remaining eggplant, sauce, mozzarella and parmesan. Bake until hot and just beginning to brown, about 20 minutes. After the 20 minute mark, if your cheese isn't nice and golden brown, crank up the oven to broil and keep a close watch on your eggplant so as not to burn it. It will broil quickly. Once to your desired cheese doneness, remove from oven.
Toss a healthy amount of grits/polenta/quinoa/rice or any other grain that you want to soak up all the goodness that's contained in this dish, on the bottom of a shallow dish or plate. Place a slice of the eggplant on top, followed by a couple spoonfuls of the gravy, and a little fresh basil or parsley for garnish.