Thinly slice the eggplant, lightly salt both sides of each piece, and lay out on the cookie sheets. Let sit for 15 minutes. Rinse the salt off each piece, setting each in the
colander after it’s rinsed.
Preheat oven to 375. Wash and dry one of the cookie sheets, then oil it. Pat each eggplant slice dry, and spread out on the cookie sheet (it’s ok if they overlap).
Cover with foil and bake for 15 minutes, until softened. Remove foil and set aside.
Place breadcrumbs, garlic, parsley, and oil in the food processor and process until minced and well blended.** Transfer to a small bowl and set aside.
Place neufchâtel, ricotta, egg, cornstarch, and a couple tablespoons of milk in the processor and blend. Scrape down the side, then start processing again as you gradually add the rest of the milk. Season with nutmeg, salt, and pepper.
Oil the baking dish, and place eggplant in the bottom. Top with tomato sauce, then the zucchini. Spread the custard on top, then sprinkle with feta, then Parmesan, then bread crumbs.
Bake about 30 minutes, until golden brown. Let sit for a couple of minutes before slicing.
*There are two ways to do this. One is to use a medium-sized baking dish, about 9×9, which will give you a taller/thicker gratin. The other is to use a very large baking dish (I used my lasagna pan, which is 11×15), which will give you a thin gratin. The taste is the same; it’s just the appearance that changes.
**If your food processor is large, this might not be enough for it to work efficiently, so you should just minced/chop everything and combine it in a bowl.
Adapted from Crescent Dragonwagon’s Passionnate Vegetarian, in which it’s called "Eggplant Gratin with Ricotta Custard and Parmesan."