Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch thick rounds, brush both sides with olive oil, and roast for 15 minutes until tender.
While eggplant roasts, brown the ground lamb in a skillet over medium heat with diced onion and minced garlic until the meat is cooked through.
Stir the tomato puree, dried oregano, sea salt, and black pepper into the lamb mixture and simmer for 5 minutes to meld the flavors.
In a small mixing bowl, whisk together the Greek yogurt and egg until the mixture is completely smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the entire lamb mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture over the top layer, spreading it evenly, and sprinkle with the crumbled feta cheese.
Bake for 20 to 25 minutes until the topping is set and develops a beautiful golden-brown color.