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 15-20 minutes until tender and slightly browned.
While the eggplant roasts, finely dice the onion and mince the garlic.
Heat a skillet over medium heat and sauté the onion and garlic until translucent and fragrant.
Add the ground beef to the skillet, breaking it up with a spatula and cooking until fully browned.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then let the mixture simmer for 5 minutes to meld the flavors.
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 slices, followed by the beef mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture evenly over the top layer of eggplant and sprinkle with the grated parmesan cheese.
Bake for 15-20 minutes until the yogurt topping is set and has developed a beautiful golden-brown color.