Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and roast for 20 minutes until tender.
While eggplant roasts, brown the ground lamb in a skillet over medium heat with diced onion and minced garlic.
Drain any excess fat, then stir in the tomato puree, cinnamon, oregano, salt, and pepper.
Simmer the lamb mixture for 10 minutes to allow the flavors to meld.
In a small bowl, whisk together the Greek yogurt and the egg until completely smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant slices followed by the lamb mixture.
Add the remaining eggplant slices on top, then pour the yogurt mixture over the eggplant to cover it.
Sprinkle with crumbled feta cheese and bake for 20-25 minutes until the topping is set and lightly browned.