Preheat your oven to 400°F (200°C).
Heat the olive oil in a large oven-safe skillet over medium heat and sauté the diced onion and cubed eggplant for 6-8 minutes until softened.
Add the ground lamb to the skillet, breaking it up with a spoon, and cook until browned and fully cooked through.
Stir in the minced garlic, tomato puree, ground cumin, cinnamon, sea salt, and black pepper, allowing the flavors to meld for 2 minutes.
In a small bowl, whisk together the Greek yogurt and the egg until completely smooth.
Spread the yogurt mixture evenly over the top of the lamb and eggplant base in the skillet or transfer to a small baking dish.
Place in the oven and bake for 15-20 minutes, or until the creamy topping is set and lightly browned on top.