Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides lightly with olive oil, and roast for 20 minutes until tender.
While the eggplant roasts, brown the ground lamb in a skillet over medium heat with the diced onion and minced garlic.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 10 minutes until the sauce has thickened.
In a separate small bowl, whisk together the Greek yogurt, egg, and nutmeg until the mixture is smooth and well combined.
Lower the oven temperature to 375°F (190°C) and lightly grease a small oven-safe baking dish.
Layer half of the roasted eggplant at the bottom of the dish, spread the lamb sauce over it, and top with the remaining eggplant.
Pour the yogurt mixture over the top layer and bake for 25 minutes until the topping is set and beautifully golden.