Get all ingredients prepped and ready to go before starting to cook. Slice the eggplant and zucchini, grate the Parmesan cheese, and slice the mozzarella cheese.
Set up a breading station for the vegetables. I like to use pie pans, but you could also use plates. You will need three. Put the flour in the first pie pan/plate and season with salt and pepper. In another pan, crack the eggs and lightly whisk in the milk, then season with salt and pepper. In a third pan/plate, stir together the breadcrumbs with 1/4 cup Parmesan cheese and season with salt and pepper.
Start breading the veggies by taking a slice of eggplant or zucchini and dredging both sides in the flour, shaking off any excess. Then repeat in the egg mix, allowing excess to drip off, and finally in the breadcrumbs. Put the breaded veggies on a plate, and repeat process with remaining slices.
Warm a large frying pan over medium high heat, and pour in olive oil to about 1/2 inch deep. When a wooden spoon inserted into the oil bubbles, the oil is ready for frying.
Place slices of veggies into the hot oil and fry for about 3-5 minutes per side until golden brown. Use tongs or a slotted spoon to remove, allowing extra oil to drain back into the pan. Move to a plate to cool and repeat process until all the eggplant and zucchini are fried.
Preheat oven to 350˚. Ladle a little tomato sauce into the bottom of a 9 x 13 baking dish or aluminum pan. Arrange eggplant and zucchini to form first layer of dish, ladle more sauce over the top, and lay slices of mozzarella and a sprinkle of Parmesan over it, repeat process 2 more times.
If you plan to freeze this dish for later, stop at this point, let cool and cover tightly with aluminum foil before transferring to the freezer.
Bake until bubbling and lightly browned on top, about 30 minutes. Allow to rest for 10 minutes, then slice and serve.