Slice the eggplant lengthwise into 4 slices. Sprinkle with salt. Place a plate on top of the eggplant and put something heavy on top of like a can of beans. Let sit for 30 minutes. Wipe salt and excess water off the eggplant slices.
In a small saucepot, add olive oil and garlic and let cook for 1 minute. Crush the tomatoes with your hand as you add them to the pot. Stir in the basil and simmer while you prepare the rest of the ingredients.
Set up a dredging station: Place the flour in one shallow bowl, the eggs in another, and add the breadcrumbs to a third.
Dip each eggplant in flour, then egg and then the breadcrumbs.
Heat the vegetable oil in a large cast-iron skillet. Add the breaded eggplant and fry for 2 to 3 minutes per side, until you have a nice rich golden crust. Remove to a paper towel-lined plate when done.
Preheat the broiler.
Cut the baguette into 4 slices horizontally, and cut each in half lengthwise. Spread some marinara on the bottom half of each piece.
Place breaded eggplant on top, add some grated Parmesan cheese, more sauce, then shredded mozzarella cheese and then more grated Parmesan.
Place the sandwiches open face in the broiler to melt the cheese. Garnish with basil leaves, top with second piece of bread and serve.