Preheat oven to 400°F. Slice 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 onions and minced garlic until the meat is cooked through.
Stir in the tomato puree, oregano, cinnamon, salt, and pepper; simmer for 5 minutes to meld the flavors.
In a small bowl, whisk together the Greek yogurt, egg, parmesan cheese, and nutmeg until the mixture is smooth.
In a small baking dish, layer the roasted eggplant and lamb sauce, then spread the yogurt mixture evenly over the top.
Bake for 20 minutes until the topping is set and lightly browned.