Place the eggplant slices in a bowl, and sprinkle with salt. Let drain over a bowl in the refrigerator for at least an hour. I like to do this overnight.
Preheat the oven to 350 degrees F (175 degrees C). Bring a large pot of lightly salted water to a boil. Add ziti pasta, and cook for about 6 minutes, or until almost tender. It will cook the rest of the way in the oven. Drain. Mix together the ricotta cheese and eggs in a small bowl. Stir in half of the mozzarella cheese and Pecorino Romano cheese.
Spread a thin layer of sauce in the bottom of a 9x13 inch baking dish. Arrange layers of eggplant, cheese, ziti pasta, and more sauce all the way to the top of the pan. Top with remaining mozzarella cheese.
Bake for 45 minutes in the preheated oven, until heated through and cheese is lightly browned.