Place the breadcrumbs, parmesan cheese, flour, dried basil, crushed red pepper, salt and pepper in a bowl and stir. Lightly beat the eggs in another bowl.
Heat a large skillet over medium heat and add the olive oil. Take the eggplant rounds and dip them in the egg, then into the breadcrumb mixture, pressing gently to adhere. Place the breaded eggplant in the skillet and cook on both sides until golden, about 2 to 3 minutes per side.
To make the grilled cheese, heat a skillet over medium-low heat. Spread the outsides of the bread slices with softened butter. Spread the insides of the bread slices with the marinara. Top one marinade side with a handful of cheese, then press a few eggplant rounds (or only one, depends on how big they are!) into the center. Top with more cheese, then the other marinara coated bread slice.
Cook the sandwich until the cheese is melted and the bread is golden and dark and toasty. Serve with extra parmesan for sprinkling and marinara sauce.