Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch rounds, brush with 0.5 tsp olive oil, and roast for 15 minutes until tender.
In a large skillet, sauté the diced onion in the remaining olive oil over medium heat until translucent.
Add the ground lamb to the skillet and cook until browned, breaking it into small crumbles with a wooden spoon.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 10 minutes to thicken.
In a small bowl, whisk together the Greek yogurt and egg until smooth to create the clean béchamel sauce.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds followed by the lamb mixture.
Place the remaining eggplant rounds on top, then spread the yogurt béchamel evenly over the surface.
Sprinkle with parmesan cheese and bake for 25 minutes until the topping is set and lightly browned.