Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with 1 teaspoon of olive oil, and roast for 15-20 minutes until tender.
While eggplant roasts, heat the remaining teaspoon of olive oil in a skillet over medium heat and sauté the diced onion and minced garlic until fragrant.
Add the ground lamb to the skillet, breaking it apart with a spatula, and cook until browned and fully cooked through.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer on low for 5 minutes.
In a small bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and well combined.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds, 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 of the dish.
Bake for 15-20 minutes until the topping is set and develops a beautiful golden-brown hue.