Preheat oven to 400°F and slice the eggplant into half-inch thick rounds.
Brush the eggplant rounds with olive oil, season with a pinch of sea salt, and roast on a parchment-lined sheet for 15 minutes until softened.
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, and oregano, then simmer for 5 minutes until the sauce has thickened.
In a small bowl, whisk together the Greek yogurt, egg, parmesan, and nutmeg until the mixture is smooth and creamy.
Layer the roasted eggplant and the lamb mixture in a small baking dish, then spread the yogurt topping evenly over the top.
Bake for 20 minutes until the topping is set and has developed a light golden brown color.