Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, lightly brush with half of the olive oil, and roast for 20 minutes until tender.
While the eggplant roasts, heat the remaining olive oil in a skillet over medium heat and sauté the diced onion and minced garlic until translucent.
Add the ground lamb to the skillet, browning it thoroughly while breaking it into small crumbles with a spatula.
Stir in the tomato puree, dried oregano, ground cinnamon, sea salt, and black pepper, then simmer for 10 minutes until the sauce has thickened.
In a small bowl, whisk together the Greek yogurt, egg yolk, parmesan cheese, and ground nutmeg until the mixture is smooth and combined.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds, followed by the spiced lamb mixture, and then the remaining eggplant.
Spread the yogurt béchamel evenly over the top layer and bake for 15-20 minutes until the topping is set and beautifully golden brown.