Cut eggplant lengthwise into strips 1/2 inch wide. Soak them for 30 minutes in a bowl of heavily salted water.
Heat oil in skillet, add the onion and cook for 5 minutes til softening, then add the tomatoes an basil and simmer gently for 30 minutes. Season with salt and pepper.
Drain eggplant, then rinse and pat dry. saute them or brush with olive oil and roast in preheated oven at 350 for about 20 minutes til deep golden brown. Set aside.
Arrange eggplant in single layer in oven dish then add a layer of grated Parmesan, followed by a layer of sliced mozzarella and a layer of the tomato sauce. Continue layering in this order til all the ingredients have been used, ending with a sauce layer. This will keep the dish moist. If you want a crisp top, end with eggplant and Parmesan
Bake in 350 oven for 30 to 35 minutes til browned and bubbling. Remove and set aside for 10 minutes to settle before serving. Serve warm or at room temperature. Serves 4