Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch rounds, brush both sides with olive oil, and roast for 15-20 minutes until tender and slightly browned.
While the eggplant roasts, heat a large skillet over medium-high heat and sauté the diced onion and garlic until translucent.
Add the ground lamb to the skillet, breaking it up with a wooden spoon, and cook until fully browned.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer on low for 10 minutes until the sauce is thick and fragrant.
In a small bowl, whisk together the Greek yogurt and the egg until smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, top with the lamb mixture, and then the remaining eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and develops a beautiful golden-brown color.