Preheat your oven to 400F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch thick rounds, brush lightly with olive oil, and roast for 20 minutes until tender.
While 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, salt, and pepper, then simmer the meat sauce for 10 minutes to thicken.
In a separate small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth and creamy.
Reduce oven heat to 375F and lightly grease a small baking dish.
Layer half of the roasted eggplant rounds in the bottom of the dish, followed by the entire lamb mixture.
Place the remaining eggplant rounds on top of the lamb and pour the yogurt custard evenly over the surface.
Bake for 25 to 30 minutes until the topping is set and develops a beautiful golden-brown color.