Wash dry and cut the eggplant into ½ cm thick slices lengthways. Sprinkle them with salt and leave them in a colander with a plate on the top as a weight so that their bitter juice is drawn out. After about an hour, squeeze the slices, rinse and pat them dry. Prepare the tomato sauce: soften the finely-chopped onion and a crushed clove of garlic in 2-3 tablespoons of olive oil. Add the tomato passata, the basil, season with salt and pepper and cook for 15-20 minutes until the sauce thickens.
Heat enough oil for shallow-frying in a frying-pan over a medium-high heat, and add the eggplant slices in a single layer. Shallow-fry on both sides for a few minutes until the slices are light golden. Remove from the pan with a slotted spoon and drain on kitchen paper. Repeat until all the eggplant slices are fried. Meanwhile, preheat the oven to 350°F.
Cut 8 oz of mozzarella into slices and keep in the fridge until ready for use. Take an oven dish and ladle a few spoons of tomato sauce into the bottom to cover the base, then arrange alternate layers of eggplant, tomato sauce, a sprinkling of grated parmesan, a little basil and the slices of mozzarella and repeat until all the ingredients are finished. Finish off with a layer of sauce and a sprinkling of Parmesan. Bake in the preheated oven for about 30 minutes. Let it rest for at least two hours then serve.