Preheat the oven to 400°F and line a baking sheet with parchment paper.
Arrange the eggplant slices on the sheet, brush with olive oil, and roast for 15 minutes until tender.
In a large skillet over medium heat, sauté the diced onion and minced garlic until soft and fragrant.
Add the ground lamb, cinnamon, oregano, sea salt, and black pepper, breaking the meat apart until fully browned.
Pour in the tomato puree and let the mixture simmer for 5 minutes to allow the flavors to meld.
In a small bowl, whisk together the Greek yogurt and the half egg until smooth and creamy.
In a small oven-safe dish, layer half the eggplant, then the lamb mixture, followed by the remaining eggplant.
Spread the yogurt mixture over the top and bake for 20 minutes until the custard is set and golden brown.