Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 0.5-inch rounds, arrange on the baking sheet, and roast for 15 minutes until softened.
Heat a non-stick skillet over medium heat and cook the ground lamb, diced onion, and minced garlic until the meat is browned.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper, then simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth for the topping.
In a small oven-safe dish, layer half the eggplant, the lamb mixture, the remaining eggplant, and spread the yogurt mixture on top.
Bake for 20-25 minutes until the topping is set and develops a beautiful golden hue.