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 and lightly brush both sides with the olive oil.
Roast the eggplant for 15-20 minutes until tender and slightly browned, then remove from the oven and reduce heat to 375°F (190°C).
In a skillet over medium heat, sauté the finely diced yellow onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, breaking it apart with a spatula, and cook until fully browned and no longer pink.
Stir in the tomato puree, sea salt, black pepper, dried oregano, and ground cinnamon, allowing the mixture to simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt and the egg until a smooth, uniform custard forms.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the spiced lamb mixture, then the remaining eggplant.
Pour the yogurt-egg mixture over the top layer, spreading it evenly with a spoon to cover the edges.
Bake for 20-25 minutes until the topping is set and develops a beautiful, bubbly golden-brown color.