Slice the eggplants into 1/4-inch thick rounds and generously salt both sides. Lay them on a rack or paper towels for about 20 minutes to draw out moisture and bitterness. Pat dry with a clean towel.
While the eggplant rests, toast the breadcrumbs in a skillet with 1 tablespoon of olive oil over medium heat until golden and crispy, about 3-4 minutes. Set aside.
Set up your dredging station: place flour seasoned with salt and pepper in a shallow bowl, beat the eggs in another bowl, and have the toasted breadcrumbs ready in a third bowl.
Dip each eggplant slice into the flour, then into the beaten eggs, and finally coat thoroughly with the toasted breadcrumbs. Place the coated slices on a plate or baking sheet.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. When shimmering, fry the eggplant slices in batches for about 2-3 minutes per side until golden brown and crispy. Drain on paper towels.
Preheat your oven to 200°C (400°F). Spread a thin layer of marinara sauce in the bottom of your baking dish. Layer some fried eggplant slices over the sauce, spoon more sauce on top, sprinkle with shredded mozzarella, and add fresh basil. Repeat until all ingredients are used, ending with a final layer of sauce and cheese.
Bake uncovered for 25-30 minutes, until the cheese is bubbling and golden. If the cheese browns too quickly, tent with foil.
Remove from oven and let rest for about 10 minutes to allow the layers to set. Garnish with additional basil if desired and serve slices warm with extra sauce on the side.