For the sauce: In a large skillet, heat the olive oil. Add the garlic and onions and season with salt and the red pepper flakes. Cook until the onions become translucent, 3 to 5 minutes. Add the sugar and the canned tomatoes. Use a wooden spoon to break up some of the whole tomatoes and cook 10 to 15 minutes over medium heat, stirring from time to time. Taste for seasoning. The tomatoes should be fairly broken down and the flavors coming together. Cook for another few minutes if the tomatoes still taste like they need a little more time to break down. Add 2 to 3 cups water to the sauce as it cooks if it looks like it's getting too thick. Set aside to cool.
For the eggplant: Arrange the eggplant rounds in a single layer on 2 baking sheets. Sprinkle with salt, on both sides of each slice, and allow it to sit for about an hour. (Salting it draws out the liquid and bitter flavor.) After an hour, rinse with cold water and dry them thoroughly with a kitchen towel.
Preheat the oven to 425 degrees F.
Put the flour in a medium bowl. In another, whisk together the eggs and milk. In a third bowl, combine the breadcrumbs with the oregano and fresh thyme leaves. Dip each eggplant slice in the flour and shake off any excess. Then, dip in the egg mixture and finally in the breadcrumbs. Make sure to coat both sides of each slice. Arrange them in single layers back on the baking sheets.
In a large skillet, pour enough oil to accumulate about 1/2-inch in the bottom. Heat the oil until it begins to smoke lightly (alternatively, test with a thermometer and wait until it registers between 380 and 400 degrees F). Use a pair of kitchen tongs to add a single layer of the eggplant to the oil. Cook them until they are golden brown, about 2 minutes on each side. Remove from the oil and transfer to a baking sheet fitted with a kitchen towel so the eggplant can drain as the others cook. Season lightly with salt. Take care to reheat the oil back up to temperature before adding another batch of slices to the pan.
To assemble: In a 17- by 11-inch baking dish, spoon about one-quarter of the tomato sauce on the bottom. Top with a layer of the fried eggplant. The eggplant slices can overlap slightly. Top with about one of the mozzarella slices. Sprinkle with about one-quarter of the Parmesan and provolone cheeses. Spoon more sauce and repeat two more times to make 3 layers. Top with the remaining mozzarella. Place the dish in the top part of the oven and cook until the cheese is melted and bubbly, 30 to 45 minutes. I always nibble on a bit of that before sharing it with my friends! Serve in a bowl so that you don't miss anything!
Recipe courtesy of Alex Guarnaschelli