Preheat your oven to 400°F (200°C).
Heat the olive oil in a medium oven-safe skillet over medium heat and sauté the diced onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, breaking it apart with a spoon, and cook until browned.
Stir in the cubed eggplant, tomato puree, cumin, cinnamon, sea salt, and black pepper, then simmer for 5-7 minutes until the eggplant begins to soften.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is completely smooth and combined.
Spread the lamb and eggplant mixture into an even layer in the skillet or transfer to a small baking dish.
Pour the yogurt and egg mixture over the top, spreading it to the edges to create a seal.
Place the dish in the oven and bake for 15-20 minutes, or until the creamy topping is set and turns a beautiful golden brown.