Place the eggplant slices in a single layer on baking sheets and sprinkle them with salt to draw out the bitter juices. After about an hour, blot with paper towels. While the bitter juices are being drawn out of the eggplant, start the marinara.
To make the marinara sauce, heat the olive oil in a large stainless-steel pot or Dutch oven over medium heat. (Do not use cast iron, which may make the sauce taste metallic due to the acidity of the tomatoes.) When the oil is hot, add the sliced garlic. Cook until the garlic becomes translucent and very fragrant. Remove the garlic from the pot.
Add the tomato puree, diced tomatoes, Italian seasoning, dried basil, red chili flakes, salt, and ground black pepper to the pot and stir to combine. Bring to a gentle boil. Then reduce the heat, cover the pot, and simmer for 25 to 30 minutes.
Taste the sauce. If it is too acidic, add 1/2 tablespoon of sugar. Taste it again and add the remaining sugar if necessary.
Prepare a breading station by setting up 3 dishes, as well as a wire rack resting on a baking sheet. Place the flour in the first dish, beat the eggs and milk together in the second dish, and place the Italian-seasoned breadcrumbs in the third dish.
Dredge an eggplant slice in the flour, dip it in the egg mixture, and dredge it in the breadcrumb mixture. Shake off any excess breading and place the eggplant on the wire rack. Repeat with the remaining eggplant.
In a large straight-sided skillet, pour the oil to a depth of 1/2 inch. Heat the oil over medium heat until it registers 400°F on a deep-frying thermometer. (The oil must be heated to 400°F so that the breaded eggplant, when added, will drop the temperature of the oil to the proper frying temperature of 375°F.)
Working in small batches, fry the eggplant slices, turning once, until golden brown. Using tongs, transfer the fried eggplant to a clean wire rack resting on a baking sheet and sprinkle with salt. Repeat with the remaining eggplant.
Preheat the oven to 400°F.
Brush a baking dish with olive oil. Cover the bottom of the dish with 1/3 of the marinara sauce. Arrange half of the eggplant over the sauce. Cover the eggplant with another 1/3 of the sauce, followed by another layer of eggplant. Sprinkle the shredded mozzarella cheese over the top.
Bake for 5 to 10 minutes, or until the cheese melts. Garnish with parsley if desired, and serve with pasta and the remaining sauce.