Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and sprinkle with a pinch of sea salt.
Roast the eggplant rounds for 15-18 minutes until they are tender and slightly browned.
While the eggplant roasts, heat a skillet over medium heat and add the ground lamb, diced onion, and minced garlic.
Cook the lamb mixture until browned, then drain any excess fat from the pan.
Stir in the tomato puree, dried oregano, ground cinnamon, and black pepper, and simmer on low for 5 minutes.
In a small mixing bowl, whisk together the Greek yogurt, egg, and grated parmesan until the mixture is smooth and well-combined.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt custard over the top layer of eggplant, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and develops a beautiful golden-brown color.