Preheat oven to 400°F (200°C).
Slice eggplant into 1/2-inch rounds, brush with 0.5 tsp olive oil, and roast for 15 minutes until tender.
In a skillet, heat remaining 0.5 tsp olive oil over medium heat and sauté diced onion and minced garlic until fragrant.
Add ground lamb to the skillet, browning it thoroughly while breaking it into small crumbles.
Stir in tomato puree, oregano, cinnamon, salt, and pepper, simmering for 5 minutes to meld flavors.
In a small bowl, whisk together the Greek yogurt and egg until smooth.
Layer the roasted eggplant in a small baking dish, top with the lamb mixture, and spread the yogurt mixture evenly over the top.
Bake for 15-20 minutes until the topping is set and lightly golden.