Start by making the sauce if you don't have any already made.
Preheat oven to 450°F. Spray 2 sheet pans with oil.
While the sauce simmers, slice the eggplant into 1/4 inch thick slices. Transfer to the prepared pans, it's ok if they overlap slightly. Season with salt. Bake for 20 minutes, turning halfway through until eggplant is golden.
Meanwhile, in a medium bowl combine ricotta, egg, parsley and 1/4 cup of grated cheese.
Put 1/2 cup sauce on the bottom of a 9x12 baking dish, add 1/3 of eggplant to cover the bottom of the dish. Top with 1/3 of the ricotta cheese mixture, 3/4 cup of the mozzarella cheese and 3/4 cup of the sauce. Add another layer of eggplant and repeat the ricotta cheese, mozzarella cheese and sauce two more times, reserving the third layer of mozzarella for topping. Finish with 1 1/2 cups of sauce, remaining mozzarella, and the remaining 2 tablespoons of grated cheese.
Heat the oven to 400F.
Cover with foil and bake until cheese is melted and everything is bubbling, about 40 minutes.
Remove foil and bake an additional 10 minutes.
Take it out of the oven and let it sit about 10 minutes before cutting.