Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch thick rounds, sprinkle with a pinch of salt, and roast for 15 minutes until tender.
While eggplant roasts, heat olive oil in a skillet over medium heat and sauté finely diced onion and minced garlic until soft.
Add the ground beef to the skillet, browning it completely while breaking it into small crumbles with a spatula.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper; simmer the meat sauce for 10 minutes to allow flavors to meld.
In a separate small bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and uniform.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the beef mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture over the top, spreading it evenly, and finish with a sprinkle of parmesan cheese.
Bake for 20 to 25 minutes until the topping is set and develops a beautiful golden-brown color.