Preheat oven to 400°F. Slice eggplant into 1/2-inch rounds, brush lightly with olive oil, and roast on a parchment-lined sheet for 20 minutes until tender.
In a skillet over medium heat, sauté diced onion and minced garlic until translucent, then add the ground lamb and cook until thoroughly browned.
Stir in the tomato puree, oregano, cinnamon, sea salt, and black pepper; simmer for 10 minutes until the sauce has thickened and flavors are melded.
In a small bowl, whisk together the Greek yogurt and egg until smooth to create a protein-rich, light béchamel topping.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds, followed by the spiced lamb mixture, and top with the remaining eggplant.
Spread the yogurt and egg mixture evenly over the top layer, sprinkle with parmesan cheese, and bake for 20-25 minutes until the top is golden and set.