Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and roast for 20 minutes until tender and slightly browned.
While eggplant roasts, brown the ground lamb in a skillet over medium heat with the diced onion and minced garlic until the meat is cooked through.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 5 minutes to thicken the sauce.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth and combined.
In a small oven-safe baking dish, layer half of the roasted eggplant, top with the lamb mixture, and finish with the remaining eggplant slices.
Spread the yogurt custard evenly over the top and bake for 20-25 minutes until the topping is set and beautifully golden.