Preheat your oven to 400°F (200°C).
In a medium skillet over medium heat, add the olive oil and sauté the minced garlic and ground lamb until the meat is browned and fully cooked.
Add the diced eggplant, cumin, coriander, cinnamon, sea salt, and black pepper to the skillet, stirring frequently for 5-7 minutes until the eggplant begins to soften.
Pour in the tomato puree and stir to combine, allowing the mixture to simmer for 5 minutes so the flavors can meld together.
Transfer the lamb and eggplant mixture into a small oven-safe baking dish, spreading it into an even layer.
In a separate small bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and pale yellow.
Pour the yogurt mixture over the lamb and eggplant, smoothing it with a spatula to cover the entire surface.
Place the dish in the oven and bake for 15-20 minutes, or until the creamy topping is set and has developed a beautiful golden-brown hue.