Preheat oven to 400°F and slice eggplant into 0.5-inch rounds.
Place eggplant on a parchment-lined baking sheet, brush with olive oil, and roast for 20 minutes until tender.
In a skillet over medium heat, brown the ground lamb with diced onion and minced garlic until the meat is cooked through.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 5 minutes.
In a separate bowl, whisk together the Greek yogurt, egg, and nutmeg until the mixture is completely smooth.
In a small baking dish, layer half of the roasted eggplant, top with the lamb mixture, and add the remaining eggplant slices.
Pour the yogurt mixture over the top and bake at 375°F for 25 minutes until the topping is set and golden brown.