Preheat oven to 400°F. Slice eggplant into 1/2-inch rounds and brush with olive oil.
Roast eggplant on a parchment-lined sheet for 20 minutes until tender.
In a skillet, sauté diced onion and minced garlic until translucent.
Add ground lamb, cinnamon, oregano, salt, and pepper, cooking until browned.
Stir in tomato puree and simmer for 5 minutes to thicken the ragu.
In a small bowl, whisk together Greek yogurt, egg, and parmesan until smooth.
In a small baking dish, layer half the eggplant, then the lamb mixture, then the remaining eggplant.
Pour the yogurt mixture over the top and bake at 375°F for 20-25 minutes until golden.