Soak eggplant in salt water for 20 minutes
Preheat the oven to 200° fan forced
Place flour on a plate. In a shallow bowl, beat eggs with a fork. On a second plate, combine bread crumbs, salt and pepper.
Dip each slice of eggplant in flour, then in the beaten egg. Let the excess egg drip off before finally dipping into the bread crumb mixture, pressing to help it adhere. Place on a clean plate.
In a large pan over medium heat, heat 1/4 cup of oil. Using tongs, add as many cutlets as can fit in a single layer (they should sizzle) and cook for about 3 minutes, or until the undersides are golden brown. Flip the cutlets and cook for 2 to 3 minutes more, until golden brown. Transfer to a paper towel-lined plate. Wipe out the skillet with paper towels and repeat with another 1/4 cup oil and the remaining eggplant.
Arrange the cutlets in a single layer on a rimmed sheet pan. Top each with a slice of tomato and a slice of mozzarella. Bake until the cheese is melted, 3 to 5 minutes.
Scatter the basil leaves over the tops and sprinkle with Parmesan and red pepper flakes.