Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Slice the eggplant into 0.5-inch thick rounds, brush both sides with olive oil, and roast for 20 minutes until tender and lightly browned.
While eggplant roasts, sauté the finely diced onion and minced garlic in a non-stick skillet over medium heat until softened.
Add the ground lamb to the skillet and cook until browned, breaking it into small crumbles with a wooden spoon.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then let the mixture simmer for 10 minutes until the liquid has reduced.
In a small mixing bowl, whisk the Greek yogurt and egg together until the texture is completely smooth and uniform.
In a small oven-safe casserole dish, layer half of the roasted eggplant, then spread the lamb mixture evenly over the top.
Place the remaining eggplant slices over the lamb, then pour the yogurt and egg mixture over the entire dish.
Sprinkle with parmesan cheese and bake for 15-20 minutes until the topping is set and golden brown.