Season eggplant slices evenly with salt and pepper. Arrange on a paper towel-lined baking sheet and let sit 15 minutes.
Meanwhile, heat ½-inch of oil in a large heavy-bottomed pot to 350°. Whisk eggs in a shallow bowl, place the flour in another shallow bowl, and the panko in another.
Pat eggplant dry, pressing between the paper towels to remove excess moisture. Dredge eggplant in flour, tapping off excess. Dip in eggs; coat with panko, patting to adhere.
Working in batches, carefully fry eggplant in oil, maintaining the temperature at or around 350, until the eggplant is tender and the crust is deep golden brown and crisp on all sides, about 7 minutes, turning halfway through. Transfer to a wire rack to cool, season immediately with salt and sprinkle with parmesan. Repeat with remaining eggplant.
Preheat the oven to broil with a rack in the top third. Arrange the buns cut side up on a rimmed baking sheet. Broil until golden about 3 to 4 minutes. Remove the top buns to plates.
Spoon a tablespoon of Rao’s Homemade® Tomato Basil sauce over each bottom bun and stack one eggplant slice on top of the sauce. Spoon another tablespoon of sauce over each eggplant slice. Top with another eggplant slice and spoon another 2 tablespoons on top of each slice. Top with provolone cheese and broil until cheese is golden and bubbly, about 3 to 4 minutes.
Top with basil and close the sandwich. Serve with extra warm tomato basil sauce.