Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush with olive oil, and roast for 15 minutes until tender.
In a skillet over medium heat, sauté the diced onion and minced garlic until translucent.
Add the ground lamb, cinnamon, oregano, salt, and pepper to the skillet, cooking until the meat is fully browned.
Stir in the tomato puree and simmer for 5 minutes until the sauce has thickened.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth.
In a small oven-safe baking dish, layer half of the eggplant rounds, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt and egg mixture over the top, spreading it evenly to the edges.
Bake for 20 minutes until the topping is set and lightly golden brown.