Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch rounds, brush with half of the olive oil, and sprinkle with a pinch of sea salt before roasting for 15 minutes until tender.
While the eggplant roasts, heat the remaining olive oil in a skillet over medium heat and sauté the diced yellow onion until translucent.
Add the ground lamb to the skillet, breaking it apart with a wooden spoon, and cook until thoroughly browned.
Stir in the minced garlic, ground cinnamon, dried oregano, sea salt, and black pepper, cooking for one minute until fragrant.
Add the tomato puree to the lamb mixture and simmer on low for 10 minutes to allow the sauce to thicken and the flavors to meld.
In a small mixing bowl, whisk together the Greek yogurt and the large egg until the mixture is completely smooth.
In a small oven-safe baking dish, create a layer using half of the roasted eggplant slices, then top with the simmered lamb mixture.
Place the remaining eggplant slices over the lamb and pour the yogurt-egg custard evenly over the top.
Bake for 20 to 25 minutes until the custard is set and the top is golden brown, then let rest for 5 minutes before serving.