Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and roast for 20 minutes until tender and lightly browned.
While eggplant roasts, brown the ground lamb in a skillet over medium heat with diced onion and minced garlic until the meat is cooked through and onions are translucent.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer on low for 10 minutes to allow the flavors to meld.
In a separate small bowl, whisk together the Greek yogurt and egg until completely smooth to create the protein-rich topping.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the spiced lamb mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture evenly over the top, sprinkle with parmesan cheese, and bake at 375°F for 20-25 minutes until the topping is set and golden.