Slice the eggplants into thin rounds and arrange them in a colander. Sprinkle lightly with salt and let them sit for about an hour to draw out excess moisture. Rinse and pat dry with paper towels.

In a saucepan, warm the olive oil over medium heat. Add the chopped onion and cook for about 5-7 minutes until soft and translucent. Stir in the crushed tomatoes and torn basil, season with salt and pepper, and let it simmer gently for 10-15 minutes. Set aside.

Heat a skillet over medium-high heat, add the ground meat, and season with salt and pepper. Cook until browned, breaking it apart as it cooks. Drain any excess fat and set aside.

Lightly coat the eggplant slices in flour. Heat the neutral cooking oil in a wide skillet and fry the slices for about a minute on each side until lightly golden. Transfer them to paper towels to drain.

Preheat the oven to 350°F (175°C). Spread a small amount of the prepared tomato sauce in the bottom of an 11x8-inch baking dish.

Layer the eggplant slices in the baking dish, sprinkle some grated cheese, add the ground meat, a few mozzarella cubes, and a spoonful of sauce. Repeat the layers until all ingredients are used, saving one-third of the sauce for topping.

Spread the remaining tomato sauce over the final layer and finish with the remaining mozzarella and grated cheese.

Cover loosely with foil and bake for 20 minutes. Remove the foil and continue baking for another 20 minutes, until the top is bubbly and lightly golden.

Let the casserole rest for 5 minutes before slicing and serving.