Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, lightly brush with half of the olive oil, and roast for 15 minutes until tender.
While eggplant roasts, heat the remaining olive oil in a skillet over medium heat and sauté the diced onion until translucent.
Add the ground lamb to the skillet, breaking it apart with a wooden spoon, and cook until browned and fully cooked through.
Stir in the minced garlic, tomato puree, cinnamon, oregano, sea salt, and black pepper, then let the mixture simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt, grated parmesan cheese, and ground nutmeg until smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, then the remaining eggplant.
Spread the yogurt mixture evenly over the top layer of eggplant and bake at 375°F for 20 minutes until the topping is set and golden.