Preheat your oven to 400°F (200°C).
Dice the eggplant into 1-inch cubes and finely chop the onion and garlic.
Heat olive oil in a skillet over medium heat; add eggplant and sauté until softened and lightly browned, about 5-7 minutes.
Add the ground lamb, onion, and garlic to the skillet, breaking up the meat with a wooden spoon until browned and cooked through.
Stir in the tomato puree, cumin, cinnamon, sea salt, and black pepper; simmer for 5 minutes to allow the flavors to meld.
Transfer the spiced lamb and eggplant mixture into a small oven-safe baking dish.
In a separate small bowl, whisk together the Greek yogurt and the egg until the mixture is completely smooth.
Pour the yogurt mixture over the lamb and eggplant, spreading it evenly to the edges.
Bake for 15-20 minutes until the creamy topping is set and develops a light golden color.