How to Make It
Salt the eggplant slices and layer them in a colander. Cover with a plate and weight down with a large can. Let stand for 30 minutes. Pat the eggplant slices dry.
Preheat the oven to 400°. In a large skillet, heat 1/8 inch of oil. Fry the eggplant slices in batches over moderately high heat until browned and tender, about 2 minutes per side. Drain on paper towels. Add more oil to the skillet as needed.
Sprinkle 2 tablespoons of the bread crumbs in a 10-inch round baking dish. Arrange half of the eggplant slices in the dish, overlapping them slightly. Spread the marinara sauce over the eggplant and arrange the hard-cooked egg slices on top. Cover with the mozzarella. Scatter the basil leaves over the cheese and season with black pepper. Arrange the remaining eggplant slices on top. Cover with foil and bake until heated through and the mozzarella is just melted, about 20 minutes.
Preheat the broiler. Uncover the baked eggplant and sprinkle the top with the remaining 2 tablespoons of bread crumbs. Drizzle with the olive oil and broil until browned, about 2 minutes. Let the eggplant rest for at least 10 minutes and up to 30. Cut into wedges and serve warm or at room temperature.