Preheat oven to 350 degrees F.
Place bread crumbs on a shallow plate. Pour egg substitute onto another shallow plate. Place a wire rack on top of a cookie sheet. Take a round of eggplant, dip it into the egg substitute until fully covered, and then drag through the bread crumbs until completely coated; transfer to a wire rack. Repeat for each round of eggplant and then bake in oven for 15 minutes.
While eggplant is baking, heat olive oil in a 5-quart nonstick saucepan over medium-high heat. Add onion and garlic and saute until soft, about 1 1/2 minutes. Add the chili flakes and stir to incorporate. Add the crushed tomatoes and tomato paste and stir to blend completely. Bring to a simmer and simmer for 5 minutes. Season with salt and pepper, stir in the basil, and remove from heat.
Remove eggplant from oven and leave oven at 350 degrees F. Line the bottom of a medium-sized casserole dish (about 13 by 11 inches) with the eggplant rounds. Pour the tomato sauce over the eggplant. Top with the cheeses. Bake for 30 minutes until cheese is soft and bubbly. Remove from oven and let stand for 5 minutes before serving.