Slice the eggplants into thick, uneven rounds about 1/2 inch thick. Lay the slices on paper towels and generously salt both sides, letting them sit for 30 minutes to draw out excess moisture and bitterness. Rinse the slices with cold water and pat dry with a towel.
Set up a breading station with a shallow bowl of beaten eggs and another with lightly toasted panko breadcrumbs mixed with dried oregano, salt, and pepper. Dip each eggplant slice into the egg wash, then coat thoroughly with seasoned breadcrumbs, pressing gently to adhere.
Heat about 3 tablespoons of olive oil in a large skillet over medium heat until shimmering. Fry the breaded eggplant slices in batches, cooking for about 2-3 minutes per side until golden brown and crispy. Transfer to paper towels to drain excess oil.
Preheat your oven to 180°C (350°F). Spread a thin layer of tomato sauce at the bottom of a large baking dish. Place a layer of fried eggplant slices over the sauce, then spoon more sauce on top, followed by a sprinkle of shredded mozzarella and parmesan cheese. Repeat the layers until all ingredients are used, finishing with a generous cheese topping.
Cover the assembled dish with foil and bake for 30 minutes, until bubbling around the edges. Remove the foil and bake for an additional 10 minutes to allow the cheese to turn golden and bubbly.
Once baked, let the dish rest for about 10 minutes to allow the layers to set. Garnish with fresh basil leaves before serving, and enjoy this hearty, rustic eggplant Parmesan with its crispy edges and melty cheese.