Preheat oven to 400°F and line a baking sheet with parchment paper.
Arrange eggplant and zucchini slices on the sheet, brush lightly with olive oil, and roast for 15 minutes until tender.
In a skillet over medium heat, brown the ground lamb with onion and garlic until the meat is fully cooked.
Stir in tomato puree, oregano, cinnamon, salt, and pepper; simmer for 5 minutes to allow flavors to meld.
In a small bowl, whisk together the Greek yogurt, egg, and half of the parmesan cheese to create the topping.
In a small baking dish, layer the roasted vegetables and lamb mixture, then spread the yogurt topping evenly over the top.
Sprinkle with the remaining parmesan and bake at 375°F for 20-25 minutes until the custard is set and golden brown.