Remove the stem and the leaves of the eggplant but don’t peel them. Cut them lengthwise into 1/4 inch (3-4) mm thick slices;
Place them into a strainer in a single layer and put it onto a big plate or directly into the kitchen sink; generously sprinkle with coarse salt;
Allow to sit for 30 minutes and then rinse off the salt in cold running water;
Pat them dry with paper towel;
Coat the eggplant slices with flour, and shake off the excess. Fry a few slices at a time in plenty of hot olive oil at 180°C (356°F) until golden crisp;
Drain them on paper towels;
Dice the fresh mozzarella and drain it to draw the water out;
Prepare the tomato sauce: wash, peel and coarsely cut the tomatoes, discard the seeds. Sauté the tomatoes in a saucepan with a little extra virgin oil;
Season with salt, pepper, fresh basil leaves and cook over medium heat without a lid for about one hour for a thick sauce;
Now assemble the parmigiana; cover the bottom of a rectangular 9 x 13-inch (25x35 cm) baking dish with a thin layer of tomato sauce; then arrange a layer of fried eggplant slices; cover the eggplant slices with tomato sauce, mozzarella cheese, ground pepper, freshly grated Parmigiano cheese, and coarsely chopped basil leaves;
Repeat this process twice with three layers of eggplant slices and two of sauce and cheese;
Top the last layer with an abundant amount of grated Parmigiano cheese and basil leaves;
Pre-heat the oven and bake at 350°F (177°C) for 30 minutes;
Let it rest a little before cutting and serving: enjoy it slowly and patiently, bite after bite.