Preheat your oven to 400°F (200°C). Slice the eggplant into 1/2-inch thick rounds.
Brush eggplant slices with olive oil and sprinkle with a pinch of sea salt. Roast on a parchment-lined baking sheet for 15-20 minutes until tender and slightly browned.
While eggplant roasts, heat a non-stick skillet over medium heat. Add the diced onion and ground lamb, breaking it up with a spatula until browned.
Stir in the minced garlic, ground cinnamon, dried oregano, sea salt, and black pepper. Cook for 1 minute until fragrant.
Add the tomato puree to the lamb mixture and simmer for 5 minutes until the sauce has thickened slightly.
In a small bowl, whisk together the Greek yogurt and the egg until smooth to create the topping.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant slices.
Pour the yogurt-egg mixture over the top, spreading it evenly to the edges.
Bake for 15-20 minutes until the topping is set and beautifully golden brown. Let rest for 5 minutes before serving.