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 both sides with half of the olive oil, and sprinkle with a pinch of sea salt.
Roast the eggplant slices for 15-20 minutes until they are tender and slightly golden, then remove from the oven and reduce the temperature to 375°F.
While the 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 spoon, and cook until browned.
Stir in the minced garlic, cinnamon, oregano, sea salt, and black pepper, cooking for 1 minute until fragrant.
Pour in the tomato puree and let the meat sauce simmer for 5-8 minutes until thickened.
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.
Pour the yogurt and egg mixture over the top, spreading it evenly to the edges, and sprinkle with the grated parmesan cheese.
Bake for 20-25 minutes until the topping is set and beautifully golden brown.