Let each eggplant start to blister, and steam, and char, turning each one a quarter turn every three or four minutes, until softened and hissing inside, the skins utterly blackened and cracked ...
Spoon enough tomato sauce to just cover the bottom of the dish, sprinkle with the Parmesan, then a single layer of eggplant. Repeat, ending with the sauce. In a warm saucepan over medium heat ...