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 lightly with olive oil, and season with a pinch of sea salt.
Roast the eggplant for 20 minutes until tender and slightly browned, then remove from the oven and reduce heat to 375°F.
In a large skillet over medium heat, brown the ground beef with the diced onion and minced garlic until the meat is cooked through.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 8 minutes until the sauce is thick and fragrant.
In a separate small bowl, whisk together the Greek yogurt and the egg until completely smooth to create the custard topping.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, top with the beef mixture, and cover with the remaining eggplant.
Pour the yogurt and egg mixture over the top layer of eggplant, spreading it evenly to the edges.
Sprinkle the grated parmesan cheese over the top and bake for 25 minutes until the custard is set and the top is golden brown.