Whisk eggs together in a deep container. Pour bread crumbs in another deep container.
Dip each slice of eggplant into the eggs, covering both sides, and press into the bread crumbs until evenly coated.
Spray a nonstick skillet with cooking spray and heat over medium heat. Arrange a layer of eggplant slices in the skillet; cook until crispy, 2 to 4 minutes. Spray tops with cooking spray and flip; continue cooking until second side is browned and eggplant is tender, 2 to 4 minutes more. Transfer to a plate. Repeat with remaining slices.
Preheat oven to 275 degrees F (135 degrees C).
Arrange a layer of eggplant slices in the bottom of a 9x13-inch baking dish. Top each slice with a basil leaf, 1 tomato slice, and 1 slice of mozzarella cheese. Place another eggplant slice on top. Cover with remaining tomato and mozzarella cheese slices.
Bake in the preheated oven until cheese is softened, but not melted, about 5 minutes.