Slice the eggplant into 1/2-inch rounds. Sprinkle both sides with kosher salt, place the slices in a colander, and let them stand for 20-30 minutes; pat very dry with paper towels.

Place the flour in one shallow bowl. In a second bowl, beat the eggs with the water, and in a third bowl combine the breadcrumbs, 1/2 cup Parmesan, Italian seasoning, and black pepper.

Coat each eggplant round in flour, dip it into the egg mixture, and press it firmly into the breadcrumb mixture. Make sure the crumbs cover both sides.

For the traditional method, heat 1/3 to 1/2 cup olive oil in a large skillet over medium to medium-high heat. Fry the breaded eggplant in batches for 2-3 minutes per side, until golden brown, then drain on a wire rack or paper towels.

For a lighter preparation, arrange the breaded slices on an oiled baking sheet, brush or spray them with oil, and bake at 425°F for about 20-25 minutes, turning once, until browned and tender.

Warm the marinara sauce. Spread a thin layer over the cut sides of the bread, then add one or two eggplant slices, a spoonful of marinara, mozzarella, Parmesan, and basil if using.

Brush the outside of each sandwich lightly with olive oil or softened butter. Cook in a preheated panini press for 4-6 minutes, until the bread is crisp and the cheese has melted.

If you do not have a panini press, cook the sandwiches in a skillet over medium heat while pressing them with a second heavy pan, about 3-4 minutes per side. Rest the panini for 1-2 minutes before slicing and serve hot with extra marinara for dipping.