Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch rounds, brush with olive oil, and roast for 15 minutes until tender.
While the eggplant roasts, brown the ground lamb in a skillet over medium heat with the finely chopped onion and minced garlic.
Stir in the tomato puree, dried oregano, and half of the sea salt and black pepper, simmering for 5 minutes.
In a small mixing bowl, whisk together the Greek yogurt, egg, and the remaining salt and pepper 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.
Pour the yogurt and egg mixture evenly over the top layer and sprinkle with parmesan cheese.
Bake for 20 minutes until the creamy topping is set and develops a light golden-brown crust.