Preheat your oven to 400°F.
In a large skillet over medium-high heat, add the olive oil and sauté the diced onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, breaking it up with a wooden spoon, and cook until browned.
Stir in the cubed eggplant, cumin, coriander, cinnamon, sea salt, and black pepper, cooking for 5 minutes until the eggplant begins to soften.
Pour in the tomato puree and simmer the mixture for another 5 minutes to allow the flavors to meld.
Transfer the lamb and eggplant mixture into a small baking dish, spreading it into an even layer.
In a small bowl, whisk together the Greek yogurt and the egg until smooth and well combined.
Pour the yogurt mixture over the lamb and eggplant, using a spatula to spread it to the edges.
Bake in the oven for 15-20 minutes until the creamy topping is set and lightly golden.