Preheat your oven to 400°F (200°C).
Slice the eggplant into 1/2-inch thick rounds, lightly brush with half the olive oil, and roast on a baking sheet for 15 minutes until softened.
While eggplant roasts, heat the remaining olive oil in a skillet over medium heat and sauté the minced garlic and ground lamb until browned.
Drain any excess fat from the skillet, then stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper; simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth.
In a small baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and lightly browned.