Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, sprinkle lightly with sea salt, and let sit for 10 minutes to draw out moisture.
Pat the eggplant slices dry, brush with 0.5 tsp of olive oil, and roast for 15 minutes until tender and slightly browned.
While eggplant roasts, heat the remaining 0.5 tsp olive oil in a skillet over medium heat and 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 fully browned.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper, then simmer for 5 minutes until the sauce has thickened.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is smooth and creamy.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt-egg mixture evenly over the top and sprinkle with the grated parmesan cheese.
Bake for 20-25 minutes until the topping is set, puffed, and beautifully golden brown.