Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant and potato into thin rounds; arrange on the baking sheet, mist with olive oil, and roast for 15-20 minutes until tender.
In a skillet over medium heat, sauté the diced onion and minced garlic in olive oil until translucent.
Add the ground lamb to the skillet, breaking it up with a spoon until browned, then drain any excess fat.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, and let the ragu simmer for 10 minutes.
In a small bowl, whisk together the Greek yogurt and egg until completely smooth to create the light béchamel sauce.
In a small oven-safe baking dish, layer the roasted potatoes, then the eggplant, followed by the lamb ragu.
Pour the yogurt béchamel over the top and sprinkle with parmesan cheese.
Bake for 20-25 minutes until the topping is golden brown and set.