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 sprinkle with a pinch of salt.
Roast the eggplant for 15 minutes until tender and slightly browned, then remove from the oven and lower the temperature to 375°F.
While eggplant roasts, heat a non-stick skillet over medium heat and brown the ground beef with the diced onion and minced garlic until the beef is cooked through.
Stir in the tomato puree, oregano, cinnamon, sea salt, and black pepper, then let the sauce simmer for 5 minutes to thicken.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth and well combined.
In a small oven-safe baking dish, place a layer of roasted eggplant, followed by the beef mixture, and then another layer of eggplant.
Spread the yogurt mixture evenly over the top layer of eggplant and bake for 20 minutes until the topping is set and golden.