Preheat your oven to 400°F (200°C). Slice the eggplant into rounds, brush with olive oil, and roast on a baking sheet for 15 minutes until softened.
While the eggplant roasts, heat a non-stick skillet over medium heat. Add the diced onion and ground lamb, cooking until the meat is browned. Drain any excess fat from the pan.
Stir in the minced garlic, tomato puree, cinnamon, dried oregano, sea salt, and black pepper. Let the mixture simmer for 5-7 minutes to allow the flavors to meld.
In a small bowl, whisk together the Greek yogurt and the egg until completely smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the lamb mixture, and then the remaining eggplant.
Spread the yogurt and egg mixture evenly over the top layer of eggplant.
Bake for 20-25 minutes until the topping is set and lightly golden brown. Let it rest for 5 minutes before serving.