Slice the eggplants into 1/2-inch thick rounds. Lightly sprinkle each slice generously with salt and set aside on a wire rack; this helps draw out moisture and bitterness. After 20 minutes, pat the slices dry with paper towels to remove excess moisture.
Set up your breading station: place flour in one shallow dish, beaten eggs in another, and seasoned panko breadcrumbs in a third. Dip each eggplant slice into the flour, then into the eggs, and finally coat thoroughly with breadcrumbs, pressing gently to adhere.
Heat about 1/4 cup of olive oil in a skillet over medium heat until shimmering. Fry the breaded eggplant slices in batches, about 2-3 minutes per side, until golden brown and slightly charred at the edges. Carefully flip with tongs and cook until crispy. Drain on a paper towel-lined plate.
Preheat your oven to 180°C (350°F). Spread a thin layer of tomato sauce on the bottom of a baking dish. Arrange a layer of fried eggplant slices over the sauce, overlapping slightly for a rustic look.
Top the eggplant layer with more tomato sauce, then sprinkle generously with shredded mozzarella. Repeat layers until all ingredients are used, finishing with a final layer of sauce and cheese on top. Sprinkle grated Parmesan over the top for added flavor.
Bake uncovered in the preheated oven for 25-30 minutes, until bubbling and the cheese is golden brown with slight charred edges, which adds flavor. Remove from oven and let rest for 10 minutes to set the layers.
Garnish with fresh basil leaves and serve slices hot, enjoying the crispy, cheesy layers with a side of extra sauce if desired. The edges should be slightly charred, and the cheese gooey and inviting.