Kuku is a Persian egg dish similar to a frittata.
Peel eggplants, reserving 4 long strips of peel to garnish top of kuku, and cut eggplants lengthwise into 1-inch-thick slices. Place on a baking sheet lined with paper towels, and sprinkle generously with salt. Turn slices over, and sprinkle again with salt. Let eggplants sit for 20 minutes. Rinse with cold water, and pat dry.
Heat broiler. Place eggplants on a rimmed baking sheet; brush both sides with olive oil. Broil about 6 inches from heat until golden brown on both sides,6 to 8 minutes per side. Transfer eggplant to a bowl, and mash with a fork; set aside.
Heat 2 tablespoons oil in a large skillet over medium heat. Add the onions and garlic; cook, stirring occasionally, until tender and golden brown, 10 to 12 minutes. Add to bowl with mashed eggplant.
Reduce oven temperature to 350 degrees. Combine eggs, parsley, saffron water, lime juice, baking powder, flour, salt, and pepper. Whisk until thoroughly combined. Add to eggplant mixture, and mix thoroughly with a fork.
Brush 1 tablespoon oil into the bottom and sides of a 9-inch springform pan. Place pan on a baking sheet, and place in the oven for 5 minutes to heat oil. Pour eggplant mixture into pan, and place the reserved eggplant peel across the top. Bake for 30 minutes. Remove pan, and drizzle remaining tablespoon oil over the top. Return to oven, and bake until golden on top, about 20 minutes more.
Transfer pan to a wire rack to cool slightly before unmolding. Cut in wedges; serve warm or at room temperature.