Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds. Brush both sides with olive oil and season with a pinch of sea salt and black pepper.
Roast the eggplant for 20 minutes, flipping halfway through, until the rounds are tender and lightly browned.
While the eggplant roasts, heat a non-stick skillet over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the garlic and ground beef to the skillet. Cook until the beef is fully browned, breaking it up with a spatula.
Stir in the tomato puree, cinnamon, and oregano. Simmer the meat sauce for 5-7 minutes until thickened.
In a small bowl, whisk together the Greek yogurt and the egg until smooth to create the topping.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the beef mixture, and then the remaining eggplant.
Spread the yogurt and egg mixture evenly over the top layer of eggplant and sprinkle with crumbled feta cheese.
Bake for 15-20 minutes until the topping is set and golden brown. Let it rest for 5 minutes before serving.