Adjust oven rack to lower-middle position and heat oven to 400 degrees.

Combine ½ cup all-purpose flour, ¼ teaspoon table salt, and ¼ teaspoon pepper together in large zipper-lock bag.

Whisk 2 large eggs together in shallow dish.

Combine 2½ cups panko bread crumbs, ½ cup grated Parmesan, remaining ½ teaspoon salt and remaining ½ teaspoon pepper in second shallow dish.

Place 1 small eggplant, sliced into ¼-inch-thick rounds, in bag of flour, shake bag to coat eggplant, then remove eggplant from bag and shake off excess flour.

Using tongs, coat floured eggplant with egg mixture, allowing excess to drip off.

Coat all sides of eggplant with bread crumb mixture, pressing on crumbs to help them adhere.

Lay breaded eggplant on wire rack set over rimmed baking sheet.

Heat ½ cup vegetable oil in 12-inch ovensafe nonstick skillet over medium-high heat until shimmering.

Add half of breaded eggplant slices to skillet and cook until well browned on both sides, 3 to 5 minutes, flipping them halfway through cooking.

Return fried eggplant to wire rack and repeat with remaining breaded eggplant.

Pour off oil left in skillet, wipe out skillet with paper towels, and let it cool slightly.

Spread 1½ cups marinara sauce over bottom of skillet.

Layer eggplant slices evenly into skillet, overlapping them slightly.

Dollop remaining ½ cup sauce on top of eggplant and sprinkle with 1 cup shredded mozzarella and remaining ¼ cup Parmesan, leaving outer 1 inch of eggplant slices clean.

Transfer skillet to oven and bake until bubbling and cheese is browned, about 15 minutes.

Let cool for 5 minutes, then sprinkle with ¼ cup chopped fresh basil and serve.