Make the sauce: In a food processor or using an immersion blender, puree the tomatoes to a smooth, creamy consistency. (If you would like a more country feel, you can wait and break them up in the pan later with a wooden spoon.)
In a large saucepan, heat the olive oil over medium-high heat until hot. Add the onion and saute 5 to 6 minutes, or until soft. Add the garlic and cook for 2 to 3 minutes, until you see the color start changing. If you¿d like to make the sauce spicy, add the red pepper flakes.
Add the tomatoes and season with kosher salt and pepper to taste. Reduce the heat to medium low and simmer for about 30 minutes. (If you did not puree the tomatoes, use a wooden spoon to break them into pieces while they cook.) Strive for balance in the consistency of the sauce. It has to be fluid, but it should not look overly wet. Add the torn basil and remove from the heat.
Meanwhile, fry the eggplant: Preheat the oven to 400 degrees F. Pour 2 inches of canola oil into a large heavy-bottomed pot or high-sided skillet. Heat over high heat until a deep-fry thermometer reads 360 degrees F. (You can also test by adding a small piece of bread to the oil. If it fries and browns, the oil is ready.) In a shallow dish, whisk together the flour, 1 teaspoon sea salt and 1/4 teaspoon pepper. Working in batches of approximately 8 slices each, dredge the eggplant slices in the flour mixture and add them to the hot oil. Fry for 1 to 2 minutes each, until browned. Using tongs, transfer the eggplant to a baking sheet lined with paper towels to let cool.
In two 9-by-13-inch baking dishes, place 1 layer of eggplant slices. Brush each with a thin layer of sauce, top with a layer of mozzarella, 2 tablespoons Parmigiano-Reggiano and a sprinkle of basil leaves. Repeat the layering two more times. Make a final layer of sauce, mozzarella and Parmigiano-Reggiano. Bake for 25 to 30 minutes, until bubbling and golden on top. Garnish with a final sprinkling of basil and Parmigiano-Reggiano and a small drizzle of olive oil.