Adjust two oven racks to the upper-middle and lower-middle positions, and place a rimmed baking sheet on each rack. Heat oven to 425 degrees.
In a large zipper-top plastic bag, add flour and pepper to taste (I like 1 teaspoon salt and 1/2 teaspoon pepper). In a second shallow dish, add eggs and beat lightly. In a third shallow dish, combine breadcrumbs, 1 cup Parmesan, 1/4 teaspoon salt, and 1/2 teaspoon pepper. Stir to combine.
Spread drained eggplant over paper towels. Wipe away as much salt as possible and press firmly on each slice to remove as much liquid as possible. Working with about 8 eggplant slices at a time, add them to the bag with the flour. Seal and shake until thoroughly coated. Remove from bag, shake off any excess flour, and dip into eggs.
Remove from eggs, allowing any excess to drop off, and coat evenly with the breadcrumbs, pressing them to adhere. Lay the breaded eggplant on a wire rack and repeating with remaining eggplant rounds.
Remove preheated baking sheets from the oven. Pour 3 tablespoons of oil onto each sheet, tilting to coat the sheets evenly. Spread breaded eggplant in a single layer over the preheated, oiled sheets.
Bake until the eggplant is well browned and crisp on the first side, about 20 minutes. Flip the eggplant slices over. Switch and rotate the baking sheets, and continue to bake until the second side is browned, about 10 minutes longer.
In the bottom of a 9-inch by 13-inch baking dish, spread 1 cup tomato sauce. Shingle half of the eggplant slices over the tomato sauce. Distribute 1 more cup of the sauce over the eggplant and sprinkle with half of the mozzarella.
Shingle the remaining eggplant in the dish and dot with another cup of the sauce, leaving the majority of the eggplant exposed so that it will remain crisp. Sprinkle with 1/4 cup of the Parmesan cheese and the remaining 1 cup of mozzarella.
Place the dish on the lower-middle rack of the oven. Bake until cheese is bubbling and well browned, about 15 minutes. Sprinkle the basil over the top and cool for 10 minutes before serving. Pass the remaining 1 cup tomato sauce and 1/4 cup Parmesan cheese separately.