Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13 inch baking dish with cooking spray.
Heat the oil in a skillet over medium heat. Place eggs and bread crumbs in 2 separate bowls. Dip eggplant slices in eggs, then in bread crumbs to coat. Fry coated eggplant slices in the skillet until golden brown. Season with salt, and drain on paper towels.
In the prepared baking dish, layer eggplant, onion, tomatoes, Parmesan cheese, and feta cheese. Top with strips of Muenster.
Bake 30 minutes in the preheated oven, until cheese is melted and bubbly.