Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds and brush both sides with half of the olive oil.
Roast the eggplant for 15-20 minutes until tender and slightly browned.
While roasting, heat the remaining olive oil in a large skillet over medium heat and sauté the onion and garlic until softened.
Add the ground lamb to the skillet, cooking until browned, and carefully drain any excess fat.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then let the mixture simmer for 10 minutes.
In a small mixing bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the custard 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.
Spread the yogurt custard evenly over the top and bake at 375°F for 20-25 minutes until the topping is set and beautifully golden.