Preheat oven to 400°F. Slice eggplant into 1/2-inch rounds and lightly brush with 0.5 tsp olive oil and a pinch of the sea salt.
Roast eggplant slices on a parchment-lined baking sheet for 15-20 minutes until tender and slightly golden.
While eggplant roasts, heat the remaining 0.5 tsp olive oil in a skillet over medium heat. Sauté diced onion and minced garlic until fragrant.
Add ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink.
Stir in tomato puree, dried oregano, cinnamon, the remaining sea salt, and black pepper. Simmer for 5-7 minutes to thicken the sauce.
In a small bowl, whisk together the Greek yogurt and egg white until smooth.
In a small oven-safe dish, layer half of the roasted eggplant, followed by the beef mixture, and the remaining eggplant.
Spread the yogurt mixture evenly over the top layer of eggplant.
Bake for 15-20 minutes until the topping is set and slightly golden. Let rest for 5 minutes before serving.