Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and roast for 15 minutes until softened.
While eggplant roasts, sauté the diced yellow onion, minced garlic, and ground lamb in a skillet over medium heat until the meat is fully browned.
Drain any excess fat from the skillet, then stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper.
Simmer the lamb mixture for 5 to 7 minutes to allow the flavors to meld and the sauce to thicken slightly.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and well combined.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the entire lamb mixture, and then the remaining eggplant slices.
Spread the yogurt and egg mixture evenly over the top layer of eggplant.
Bake for 20 to 25 minutes until the yogurt topping is set and has turned a light golden brown.