Heat the olive oil in a medium saucepan over medium-high heat. Saute the onion and garlic, stirring, until lightly browned (about 3 minutes). Add the roughly chopped tomatoes (and tomato juice that was set aside) and the herb sprigs. Bring to a boil. Lower the heat to let simmer, while preparing and frying the eggplant. Cover and stir occasionally.
2Remove and discard the herb sprigs before adding to eggplant. Stir in the salt and season with pepper to taste.
Slice eggplant approx. 1/2 in. thick. Arrange the eggplant slices on several baking sheets and sprinkle generously all over both sides with coarse sea salt. Set aside to let the bitter juices bleed from eggplant slices for at least 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.
4Put flour in a medium shallow bowl. In another medium bowl, whisk the egg and milk together. Dredge an eggplant slice in the flour, then dip it in the egg, and finally dredge it in the breadcrumb mixture. Shake off excess bread crumbs from eggplant and place on large plate. Repeat with the remaining eggplant.
5In a large skillet, pour the oil into pan until it covers the bottom of skillet (about 1/2 in. deep). Heat the oil over medium heat (about 400 degrees - you can check temp with a deep fryer thermometer).
Working in small batches, fry the eggplant slices, turning once, until golden brown, about 3 minutes per batch. Using tongs, transfer to a paper towel-lined baking sheet and season with salt to taste. Repeat with the remaining eggplant.
6Preheat the oven to 375 degrees F. Lightly brush a 15 x 10- x 2-inch-baking dish with olive oil. Cover the bottom of the baking dish with 1/3 of the marinara sauce and arrange half of the eggplant over the sauce. Cover the eggplant with another 1/3 of the sauce. Scatter half of the Parmesan and half of the mozzarella over the sauced eggplant. Repeat with the remaining eggplant, sauce, Parmesan, and mozzarella. Bake until hot and just beginning to brown, about 45 minutes. Serve immediately.