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 season with a pinch of salt.
Roast the eggplant for 15-20 minutes until tender and slightly browned, then remove from the oven and reduce heat to 375°F.
While eggplant roasts, heat a non-stick skillet over medium heat and add the ground lamb, diced onion, and minced garlic.
Sauté until the lamb is fully browned and the onions are translucent, draining any excess fat if necessary.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper; simmer on low for 5-7 minutes until the sauce thickens.
In a small mixing bowl, whisk together the Greek yogurt and egg until completely smooth and combined.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds to cover the bottom.
Spread the lamb mixture evenly over the eggplant layer, then top with the remaining eggplant rounds.
Pour the yogurt and egg mixture over the top, spreading it to the edges, and sprinkle with parmesan cheese.
Bake for 20-25 minutes until the topping is set and has developed a beautiful golden-brown crust.