Preheat oven to 400°F. Slice eggplant into 1/2-inch rounds, brush lightly with olive oil, and roast for 15-20 minutes until tender.
In a skillet over medium heat, sauté diced onion and minced garlic until translucent.
Add the ground lamb to the skillet, browning it thoroughly and draining any excess fat.
Stir in tomato puree, cinnamon, oregano, salt, and pepper; simmer for 10 minutes until the sauce thickens.
In a small bowl, whisk together the Greek yogurt, egg white, parmesan, and nutmeg to create the topping.
In a small baking dish, layer half the eggplant, followed by the lamb mixture, and the remaining eggplant.
Spread the yogurt mixture evenly over the top and bake for 20-25 minutes until the custard is set and lightly browned.