Preheat your oven to 400°F (200°C).
Slice the eggplant into 1/2-inch rounds. Brush with olive oil and sprinkle with a pinch of sea salt, then roast on a baking sheet for 15 minutes until softened.
While the eggplant roasts, heat a skillet over medium heat and brown the ground lamb with the diced onion and minced garlic until the meat is cooked through.
Stir in the tomato paste, cumin, cinnamon, remaining salt, and black pepper, cooking for 2 more minutes to meld the flavors.
In a small bowl, whisk together the Greek yogurt and the egg until smooth and creamy.
In a small oven-safe baking dish, layer the roasted eggplant rounds and top with the spiced lamb mixture.
Pour the yogurt-egg mixture evenly over the lamb, spreading it to the edges.
Bake for 15-20 minutes until the topping is set and lightly browned. Garnish with fresh chopped parsley before serving.