1. Heat the oven to 350 degrees F. Heat 1 tablespoon oil in a small- to medium-sized, deep, heavy saucepan over medium heat. When the oil is hot, add the garlic and saute until it's aromatic and softened, about 1 minute. Add the tomatoes, oregano, orange juice, 1/2 teaspoon salt, a pinch of pepper, and the red pepper flakes, and raise the heat to medium high. Simmer until the mixture is reduced by about a third, about 20 minutes, using a potato masher to crush the tomatoes a bit (you should yield about 2 1/2 cups sauce). Remove and discard the oregano sprigs, and set the sauce aside.
2. Lay the eggplant rounds in one layer on a cutting board. Season both sides evenly with a total of 1 teaspoon salt and about 1/8 teaspoon pepper. Pour the flour into a medium-sized bowl. In a second medium-sized bowl, whisk the eggs well with 2 tablespoons water until smooth. In a large bowl, combine the panko, 1 cup grated Parmigiano-Reggiano, the lemon zest, 1/4 teaspoon salt, and the remaining pepper. Arrange the bowls in this order: flour, eggs, and panko.
3. Using tongs, dip an eggplant round in flour to coat both sides and then shake off any excess. Transfer to the egg mixture and coat both sides, shaking off any excess. Transfer to the panko mixture and coat both sides, shaking off any excess. Set aside on a large surface. Repeat with all of the eggplant rounds.
4. Line a large baking sheet or cutting board with paper towels. Heat 1/2 cup oil in a 12-inch, heavy, nonstick saute pan with relatively high sides over medium-high heat. When the oil is hot but not smoking, add about 5 rounds of eggplant, and cook, turning over halfway through, until both sides are golden brown, about 6 minutes. Transfer to the paper towel-lined surface to degrease. Repeat with the remaining eggplant, in batches, using about another 1/4 cup plus 2 tablespoons oil total (make sure there is always a thin layer of oil in the pan).
5. Once you've finished frying the eggplant, grease the inside of an 8 x 8-inch square baking dish with the remaining 1 tablespoon oil, and place the baking dish on a baking sheet with sides. Pour a third of the sauce (about 3/4 cup) into the bottom of the dish. Add half of the eggplant rounds, laying them flat and overlapping them as needed. Sprinkle evenly with 1/2 cup shredded mozzarella. Ladle another third of the sauce evenly atop the cheese. Then place the remaining eggplant rounds on top, overlapping them to fit. Sprinkle with the remaining 1/2 cup shredded mozzarella, ladle on the remaining sauce, and then arrange the sliced fresh mozzarella on top to cover. Sprinkle the top with the remaining 1/2 cup grated Parmigiano-Reggiano.
6. Bake, uncovered, until all of the cheese melts and turns a light golden brown, about 35 minutes. Serve, garnishing each portion with some fresh basil.