Wash and dry the eggplants. Slice off the cap end and then slice the eggplants lengthwise into half centimeter thick slices.
Arrange the slices in a colander and sprinkle them with lightly coarse salt. Sprinkle coarse salt on every eggplant layer.
Cover the eggplants layers with a pot full of water.
Set aside for 30 minutes to let the salt draw out the excess of bitter water.
Heat 2 tbsp of olive oil in a large pot and add the clove of garlic (NOT minced). Add tomato sauce and season to taste with salt.
Add a glass of water and ten or fifteen fresh basil leaves.
Cover and simmer over low heat for fifteen to twenty minutes, until the sauce is slightly thickened.
Wash the eggplant under current water to let the salt go away and let them dry on a dish cloth. Cove over with another dish cloth and set aside for half an hour.
Fill a small pan to half with vegetable oil
Heat it over medium heat. Whet it's hot fry the eggplant slices two to three at a time, until well browned.
Remove each fried slice, let it drain on a paper-towel lined plate or tray.
Adjust the burner temperature and oil level as you fry to keep them constant.
Preheat oven at 180°C
Cover the bottom of a 40 by 26 centimeters rectangular baking dish with a thin layer of tomato sauce, then cover that layer of sauce with a layer of fried eggplant slices.
Cover the eggplants with a layer tomato sauce, then a generous sprinkling of grated Parmigiano-Reggiano, then pieces of scamorza or mozzarella distributed evenly.
Cover the mozzarella with another layer of eggplant, then tomato sauce, Parmigiano, basil, mozzarella and another layer of eggplant.
Repeat until ingredients are used up. The top layer should be a layer of tomato sauce topped with a final sprinkling of grated Parmigiano
Bake for 30 minutes.
Let it rest for at least three hours. The best you can do it's to prepare eggplant parmigiana the day before you will consume it (it tastes better the next day)