Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides lightly with olive oil, and sprinkle with a pinch of sea salt.
Roast the eggplant for 15-18 minutes until tender and slightly browned, then remove from the oven and lower the temperature to 375°F.
While eggplant roasts, heat a skillet over medium heat and add the ground lamb, diced onion, and minced garlic.
Sauté until the lamb is browned and the onions are translucent, draining any excess fat if necessary.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper, then simmer the meat sauce for 5-7 minutes to meld the flavors.
In a small mixing bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth and combined.
In a small oven-safe baking dish, layer half of the roasted eggplant slices to cover the bottom.
Spread the lamb mixture evenly over the eggplant, then top with the remaining eggplant slices.
Pour the yogurt and egg mixture over the top, spreading it to the edges, and bake for 20-25 minutes until the topping is set and golden brown.