Preheat your oven to 400°F (200°C). Slice the eggplant and potato into thin rounds.
Place eggplant and potato slices on a baking sheet lined with parchment paper, brush lightly with half the olive oil, and roast for 15-20 minutes until tender.
While vegetables roast, heat the remaining olive oil in a skillet over medium heat. Sauté the diced onion and minced garlic until translucent.
Add the ground lamb to the skillet, breaking it up with a spoon, and cook until browned. Drain any excess fat.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper. Simmer for 10 minutes to allow the flavors to meld.
In a small bowl, whisk together the Greek yogurt, egg whites, and parmesan cheese to create the topping.
In a small oven-safe dish, layer the roasted potatoes at the bottom, followed by the lamb mixture, and then the roasted eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the topping is set and lightly golden. Let rest for 5 minutes before serving.