Preheat your oven to 400°F (200°C).
Heat the olive oil in a large oven-safe skillet over medium heat and sauté the cubed eggplant until it is softened and lightly browned.
Add the ground lamb to the skillet, breaking it up with a wooden spoon, and cook until the meat is browned through.
Stir in the minced garlic, cumin, cinnamon, oregano, sea salt, and black pepper, cooking for about 1 minute until highly fragrant.
Pour in the tomato puree and simmer the mixture for 3-5 minutes until it has thickened slightly.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is completely smooth.
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, using a spatula to spread it evenly to the edges.
Place the dish in the oven and bake for 15-20 minutes until the creamy topping is set and develops a beautiful golden hue.