Trim the ends off each eggplant and slice crosswise into rounds about 1/2 inch thick. Lay the slices in a single layer on paper towels or in a colander, and sprinkle both sides with the 2 teaspoons of kosher salt.
Let the eggplant rest for 30 minutes to draw out excess moisture and bitterness. Pat each slice dry with fresh paper towels before moving on.
Heat 2 tablespoons of the olive oil in a saucepan over medium heat. Add the minced garlic and cook, stirring often, until fragrant, about 1 minute.
Pour in the San Marzano crushed tomatoes, then season with salt and pepper. Simmer the sauce for 15 to 20 minutes, stirring occasionally, until it thickens slightly. Stir in the torn basil leaves during the last few minutes of cooking, then set the sauce aside.
Place the flour in one shallow bowl, the beaten eggs in a second bowl, and the panko breadcrumbs in a third bowl. Stir the dried oregano and garlic powder into the breadcrumbs, along with 1/2 cup of the grated Parmigiano Reggiano.
Working one slice at a time, dredge the eggplant in the flour and shake off the excess. Dip the floured slice into the beaten eggs, letting any extra egg drip off. Press the slice into the breadcrumb mixture on both sides, patting gently so the crumbs stick. Set each breaded slice on a baking sheet or tray.
For frying, heat the remaining olive oil in a large skillet over medium heat until shimmering, then fry the breaded slices in batches for 2 to 3 minutes per side, until deep golden brown. Transfer to a wire rack to drain.
For baking, preheat the oven to 400°F, arrange the breaded slices on a baking sheet brushed with olive oil, and bake for 20 to 25 minutes, flipping halfway through, until golden and crisp.
Preheat the oven to 375°F. Spread a thin layer of marinara across the bottom of the 9x13 inch baking dish. Arrange a layer of the browned eggplant slices over the sauce, overlapping slightly.
Spoon more marinara over the eggplant, then add slices of the fresh mozzarella and a sprinkle of the remaining Parmigiano Reggiano. Repeat the layers until all the eggplant, sauce, and cheese are used, finishing with a top layer of mozzarella and parmesan.
Cover the dish loosely with foil and bake for 20 minutes. Remove the foil and bake for another 10 to 15 minutes, until the cheese is melted and golden in spots.
Let the dish rest for 10 minutes before slicing, so the layers set and hold together. Garnish with fresh basil leaves before serving.