Preheat your oven to 375°F (190°C).
Heat the olive oil in a large oven-safe skillet over medium heat and sauté the cubed eggplant until it begins to soften and brown slightly.
Add the ground lamb to the skillet, breaking it up with a wooden spoon, and cook until browned through and no longer pink.
Stir in the ground cumin, garlic powder, ground cinnamon, sea salt, and black pepper, ensuring the meat and eggplant are evenly coated and fragrant.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and well combined.
Spread the lamb and eggplant mixture into an even layer in the skillet, or transfer to a small baking dish if preferred.
Pour the creamy yogurt and egg mixture over the top, using a spatula to spread it evenly to the edges.
Bake for 15 to 20 minutes, or until the yogurt topping is set and develops a light golden hue.
Remove from the oven and garnish with freshly chopped parsley before serving hot.