Prepare the Eggplant:
Sprinkle eggplant slices with salt and let rest on a wire rack for 15 minutes. Pat dry, spray with olive oil, and roast at 475°F (245°C) for 15-20 minutes, flipping halfway through.
Prepare the Potatoes:
Microwave whole potatoes with a splash of water, covered, for 12-14 minutes until fork-tender. Peel and slice into 1/2-inch rounds.
Make the Lamb Filling:
In a large skillet, sauté onion and garlic until soft. Add lamb and brown thoroughly. Stir in tomato paste, cook for 1 minute, then deglaze with wine if using. Add crushed tomatoes, oregano, cumin, cinnamon, salt, and pepper. Simmer uncovered for 10-12 minutes.
Make the Yogurt Topping:
In a bowl, mix Greek yogurt, grated cheddar, beaten eggs, salt, and pepper until smooth.
Assemble:
Lower oven to 425°F (220°C). Layer potatoes in the base of a 9×13 dish. Spread lamb filling over potatoes, layer roasted eggplant on top, then pour yogurt topping over. Sprinkle with parmesan.
Bake:
Bake for 20-25 minutes until golden and bubbling. Let rest for 10-15 minutes before serving.