Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice eggplant into 1/2-inch rounds, lightly brush with olive oil, and roast for 15 minutes until tender.
In a skillet over medium heat, brown the ground lamb with diced onion and minced garlic until the meat is no longer pink.
Stir in tomato puree, cinnamon, oregano, sea salt, and black pepper, allowing the mixture to simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt and egg until the custard is completely smooth.
In a small oven-safe baking dish, layer half the eggplant, followed by the lamb mixture, the remaining eggplant, and finally the yogurt custard.
Bake for 15 to 20 minutes until the custard topping is set and develops a beautiful golden hue.