Preheat the oven to 425°F. Cut the eggplants into 4-inch (10-cm) thick slices and layer them in a colander, sprinkling each layer with some of the salt. Let stand for 30 minutes, then rinse the slices and drain them well. Place them on baking sheets lined with parchment paper and roast, in batches if necessary, for about 20 minutes or until tender. Set aside.
Heat the oil in a large, shallow Dutch oven or deep nonstick skillet over medium heat. Add the onions, garlic, red and green peppers, oregano, cinnamon, pepper and allspice and cook until the onions have softened, about 5 minutes. Add the tomatoes and tomato paste and bring to a boil. Add the chickpeas and parsley, reduce the heat, and simmer for 15 minutes.
Make the Cheese Sauce: Heat the oil in a saucepan over medium heat. Stir in the flour and cook for 1 minute. Whisk in the milk and cook, whisking gently, for about 10 minutes or until the mixture is thick enough to coat the back of a spoon. Stir in the salt, nutmeg and black pepper. Let cool slightly and whisk in the egg and cottage cheese.
Preheat the oven to 350°F. Spread one-third of the tomato sauce on the bottom of a 9x13 inch baking dish. Top with one-third of the eggplant slices and one quarter of the feta cheese. Repeat the layers. After the last layer of eggplant, spread the cheese sauce evenly over the top and sprinkle with the remaining feta.
Bake for about 1 hour or until the top is golden brown. Let stand for 10 minutes before serving.