Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into rounds, brush with olive oil, and roast for 15 minutes until tender.
In a skillet over medium heat, brown the ground lamb with diced onion and minced garlic until cooked through.
Stir in the tomato puree, oregano, cinnamon, salt, and pepper, then simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt, egg, parmesan, and nutmeg to create the topping.
In a small baking dish, layer half the eggplant, all of the lamb mixture, the remaining eggplant, and finally the yogurt topping.
Bake for 20-25 minutes until the top is set and lightly browned.