Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into half-inch thick rounds, sprinkle lightly with sea salt, and let sit for 10 minutes before patting dry.
Arrange the eggplant slices on the baking sheet, brush with 1 teaspoon of olive oil, and roast for 15 minutes until tender.
While the eggplant roasts, heat the remaining teaspoon of olive oil in a skillet over medium heat.
Sauté the diced onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, browning it thoroughly while breaking it into small crumbles with a wooden spoon.
Stir in the tomato puree, dried oregano, cinnamon, sea salt, and black pepper, then simmer for 5 minutes.
In a small mixing bowl, whisk together the Greek yogurt and egg white until the mixture is completely smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the entire lamb mixture.
Top with the remaining eggplant slices, then spread the yogurt béchamel evenly over the surface.
Sprinkle the grated parmesan cheese over the top and bake at 375°F for 20 minutes until the topping is set and golden brown.