Salt the eggplant: Arrange the eggplant rounds in a single layer on a baking sheet or rack. Sprinkle both sides lightly with salt and let sit for 30 minutes to draw out excess moisture. Pat very dry with paper towels.
Heat the oven: Preheat oven to 375°F (190°C). Line two large baking sheets with parchment paper and lightly brush or spray with olive oil.
Set up breading: Place flour in one bowl, beaten eggs in a second bowl, and breadcrumbs in a third bowl.
Bread the eggplant: Dip each slice in flour (shake off excess), then egg, then breadcrumbs. Lay on prepared baking sheets. Lightly brush or spray the tops with olive oil.
Bake the eggplant: Bake for 20–25 minutes, flipping halfway through, until crisp and golden.
Assemble: Spread a thin layer of tomato sauce in the bottom of a 9x13-inch baking dish. Add a layer of baked eggplant, then spoon on more sauce. Sprinkle with mozzarella and parmesan (and add small dollops of ricotta if using). Add a few basil leaves. Repeat layers until ingredients are used, finishing with sauce and a generous layer of cheese on top.
Bake: Bake uncovered for 25–30 minutes, until the cheese is melted and deeply golden and the sauce is bubbling around the edges.
Rest and serve: Let stand for 10 minutes before slicing so the layers set. Top with fresh basil and a drizzle of extra-virgin olive oil if desired.