Preheat your oven to 400°F (200°C).
Heat the olive oil in a skillet over medium heat and sauté the diced onion, minced garlic, and cubed eggplant until they begin to soften.
Add the ground lamb to the skillet and cook until browned, breaking it into small crumbles with a spoon.
Stir in the tomato puree, cumin, cinnamon, sea salt, and black pepper, then let the mixture simmer for about 5 minutes until the sauce thickens.
Transfer the lamb and eggplant mixture into a small oven-safe baking dish.
In a separate bowl, whisk together the Greek yogurt and the egg until smooth and well combined.
Spread the yogurt mixture evenly over the lamb to create a thick top layer.
Bake for 15 to 20 minutes until the creamy topping is set and turns a light golden brown.