Lay the eggplant slices in a colander and season both sides with the tablespoon of salt. Let them rest for 30 minutes (or up to 3 hours) to draw out excess moisture, then blot dry with paper towels.

Preheat the oven to 350°F (175°C) and lightly grease a baking sheet.

In a shallow bowl combine the bread crumbs with 1/4 cup of the grated Parmesan. In a separate shallow bowl whisk the beaten eggs.

Working one slice at a time, dip an eggplant slice into the beaten eggs, let excess drip off, then press it into the breadcrumb mixture to coat both sides. Place the coated slices in a single layer on the prepared baking sheet.

Bake the breaded eggplant until lightly browned and crisp, about 5 minutes per side. Remove from the oven and set aside.

Spread a thin layer of the garlic-tomato sauce across the bottom of a 9x13-inch casserole dish. Arrange a layer of baked eggplant over the sauce, sprinkle about 1 tablespoon of the remaining Parmesan and one-third of the mozzarella. Repeat layers with the remaining eggplant, sauce, Parmesan, and mozzarella, finishing with a top layer of cheese. Sprinkle dried basil over the assembled dish.

Bake the assembled casserole in the preheated oven until the cheese is melted, bubbling, and golden on top, about 35 minutes. Let the dish rest a few minutes before serving.