Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch rounds, brush with 0.25 tbsp of the olive oil, and roast for 15 minutes until tender.
While the eggplant roasts, heat the remaining 0.25 tbsp olive oil in a skillet over medium heat.
Sauté the diced onion and minced garlic until fragrant and translucent.
Add the ground lamb to the skillet, browning it completely while breaking it into small crumbles.
Stir in the tomato puree, dried oregano, ground cinnamon, sea salt, and black pepper, then simmer for 8-10 minutes.
In a small bowl, whisk together the Greek yogurt and egg until the mixture is smooth and well combined.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant.
Spread the yogurt mixture evenly over the top and sprinkle with the grated parmesan cheese.
Bake for 20 minutes until the topping is set and develops a beautiful golden-brown color.