Preheat your oven to 400°F (200°C).
Slice the eggplant into 0.5-inch thick rounds, brush both sides with olive oil, and roast on a baking sheet for 15 minutes until tender.
While eggplant roasts, finely dice the onion and mince the garlic.
In a non-stick skillet over medium heat, cook the ground lamb, onion, and garlic until the meat is browned and onions are translucent.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer on low for 5 minutes.
In a small mixing bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges.
Bake for 20 minutes or until the topping is set and develops a light golden-brown color.