Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant and potato into 1/4-inch thick rounds, brush lightly with olive oil, and roast for 15 minutes until tender.
In a non-stick skillet over medium heat, sauté the diced onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, browning it thoroughly while breaking it into small crumbles, then drain any excess fat.
Stir in the tomato puree, dried oregano, cinnamon, sea salt, and black pepper, and simmer the meat sauce for 5-7 minutes.
In a small mixing bowl, whisk together the Greek yogurt and egg yolk until completely smooth and combined.
In a small individual oven-safe baking dish, layer the roasted potato slices at the bottom, followed by the lamb mixture, and then the eggplant slices.
Spread the yogurt and egg mixture evenly over the top layer of eggplant and sprinkle with the grated parmesan cheese.
Bake for 15-20 minutes until the topping is set and has developed a beautiful golden hue.