Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice eggplant into 1/2-inch rounds, brush both sides with olive oil, and roast for 15 minutes until tender and slightly browned.
While eggplant roasts, sauté diced onion and minced garlic in a non-stick skillet over medium heat until fragrant.
Add ground lamb to the skillet, breaking it up with a spatula until fully browned, then drain any excess liquid.
Stir in tomato puree, cinnamon, oregano, sea salt, and black pepper, allowing the sauce to simmer for 8-10 minutes.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth.
In a small oven-safe dish, layer half of the roasted eggplant, top with the lamb mixture, and finish with the remaining eggplant.
Pour the yogurt mixture over the top, spreading evenly, and bake for 20 minutes until the topping is set and beautifully golden.