Preheat oven to 375˚F. Ready a baking sheet with parchment paper and then spray with cooking spray. Set aside.
In a mixing bowl, combine Panko breadcrumbs and grated Parmesan.
Slice each eggplant into 9 rounds. Coat with beaten egg, then breadcrumb mixture. Arrange eggplant slices in a single layer on baking sheet about 1 1/2 inches apart. Bake for about 15 minutes, until browned, then flip and bake for another 10 minutes. Remove from oven.
Eggplant will be hot! Using a thin spatula, carefully layer each stack on the baking sheet: one slice of baked eggplant, a generous tablespoon of fresh mozzarella, another slice of eggplant and a spoonful of fresh mozzarella. Top it with a final slice of eggplant, a hearty drizzle of tomato sauce and a sprinkling of shredded mozzarella. Continue to layer in this manner. Bake for another 5 to 10 minutes to melt cheeses.
Sprinkle with basil. Allow stacks to rest for about 2 minutes before serving.