Preheat oven to 400 degrees F. Fit 2 baking sheets with cooling racks.
Cut the eggplant into round slices about 1/2-inch thick and place on the prepared baking sheets.
Combine the olive oil and garlic in a small bowl and mix well. Pat the eggplant slices dry, brush each slice with the olive oil mixture and season with salt. Place the eggplant in the oven to roast until just tender, about 8 minutes.
Remove from the oven and working one at a time, spread 1 to 2 teaspoons marinara sauce over each eggplant slice. Add a slice of mozzarella and another spoonful of marinara. Place another slice of roasted eggplant on top and gently press together. Set aside and repeat until all the eggplant has been used.
Set up 3 bowls or shallow dishes on the countertop – one with flour and 1 teaspoon salt, one with beaten eggs, milk and 1 teaspoon salt and the third with breadcrumbs and 1 teaspoon salt.
Carefully take the assembled eggplant stacks and dip them into flour, then the egg making sure that all sides are completely coated. Roll in the breadcrumbs, again taking care to cover all sides. Set aside on a clean baking sheet while the remaining pieces are breaded.
Pour oil into a large cast-iron pan to a depth of 3/4-inch. Heat the oil to 375 degrees F.
Carefully add the eggplant pieces, 3 or 4 at a time, and fry until golden brown, 3 to 5 minutes. Drain on a cooling rack and rest for 1 minute before transferring to a plate to serve. Repeat with the remaining eggplant stacks. Sprinkle with Parmesan and serve with extra sauce on the side.