Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and sprinkle with a pinch of sea salt.
Arrange the eggplant on the baking sheet and roast for 15 minutes until the flesh is tender and slightly browned.
While eggplant roasts, place a skillet over medium heat and add the ground lamb and finely diced yellow onion.
Cook the lamb until browned, breaking it up with a wooden spoon, then stir in the minced garlic, cumin, cinnamon, sea salt, and black pepper.
Pour in the tomato puree and simmer the meat mixture for 5 minutes until the sauce has thickened and coated the lamb.
In a separate small bowl, whisk together the Greek yogurt and the egg until the mixture is completely smooth and combined.
Lightly grease a small oven-safe baking dish or ramekin with a touch of oil.
Place half of the roasted eggplant rounds in the bottom of the dish, then layer the spiced lamb mixture over the top.
Add the remaining eggplant rounds as a second layer and pour the yogurt-egg mixture evenly over the entire dish.
Place the dish in the oven and bake for 20 minutes until the creamy topping is set and develops a light golden hue.
Remove from the oven and let the bake rest for 5 minutes to allow the layers to set before serving warm.