Slice eggplants into [1/4]-inch slices, sprinkle evenly with 1 teaspoon salt, and place in a strainer to drain for 30 minutes.
In a large skillet over medium heat, heat 3 tablespoons extra-virgin olive oil. Add white onions and [1/2] teaspoon salt, and cook for 5 minutes.
Add garlic and chickpeas, and cook for 3 minutes.
In a 2-quart pot over medium-low heat, combine tomato sauce, remaining 1 teaspoon salt, sugar, black pepper, cayenne, allspice, and nutmeg. Simmer for 10 minutes.
Preheat a large skillet over medium heat, and add remaining [1/4] cup extra-virgin olive oil.
Pat each piece of eggplant dry with a paper towel, and place eggplant in the skillet. Do not overcrowd. Cook for 3 minutes per side, and transfer to a plate lined with paper towels to drain.
In a small bowl, combine breadcrumbs and Parmesan cheese. Set aside.
Preheat the oven to 400ºF.
To assemble, ladle a spoonful of tomato sauce on the bottom of a deep casserole dish. Add a layer of eggplant, a layer of tomatoes, a layer of onion mixture, and another layer of sauce. Repeat layering, finishing with a layer of eggplant and tomato sauce. Top with breadcrumb mixture, cover with aluminum foil, and bake for 40 minutes.
Remove the foil and let breadcrumbs brown for 5 to 7 minutes.
Remove casserole from the oven, and let sit for 20 minutes before serving.
Notes
Healthy Hint This dish is nutritional because it contains protein from the chickpeas; antioxidants from the garlic, onions, and tomatoes; plus carotenoids from the tomatoes.