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 olive oil, and roast for 15 minutes until softened.
While eggplant roasts, brown the ground beef in a skillet over medium heat with the diced onion and minced garlic.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper, then simmer for 5 minutes to thicken the sauce.
In a small mixing bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the texture is smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the beef mixture, and then the remaining eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and has turned a beautiful golden brown.