Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds and lightly brush both sides with olive oil.
Roast the eggplant for 15-20 minutes until tender and slightly browned.
While eggplant roasts, sauté the onion and garlic in a skillet over medium heat until fragrant.
Add the ground lamb to the skillet, breaking it apart and cooking until fully browned, then drain any excess fat.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 10 minutes.
In a small bowl, whisk together the Greek yogurt, egg white, and parmesan cheese until smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and then the remaining eggplant.
Spread the yogurt mixture evenly over the top and bake for 20 minutes until the topping is set and golden.