Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 0.5-inch thick rounds, lightly brush with olive oil, and roast for 15-20 minutes until tender.
While eggplant roasts, brown the ground lamb in a skillet over medium heat, breaking it into small crumbles.
Add the diced onion and minced garlic to the lamb, sautéing for 3-4 minutes until the onion is translucent.
Stir in the tomato puree, oregano, cinnamon, sea salt, and black pepper, then simmer for 5 minutes to meld the flavors.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth.
In a small baking dish, layer half of the eggplant slices, top with the lamb mixture, and then the remaining eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and lightly browned.