Preheat your oven to 400°F (200°C).
Dice the eggplant into small cubes and finely chop the yellow onion and garlic.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Add the eggplant cubes and sauté for 5-7 minutes until they begin to soften and brown.
Add the ground lamb to the skillet with the eggplant, breaking it up with a wooden spoon. Stir in the onion and garlic.
Season the mixture with ground cumin, cinnamon, sea salt, and black pepper. Cook until the lamb is browned and the onions are translucent.
In a small bowl, whisk together the Greek yogurt and the egg until completely smooth.
Spread the lamb and eggplant mixture evenly across the bottom of the skillet (or transfer to a small baking dish).
Pour the yogurt and egg mixture over the top, spreading it to the edges to create a seal.
Place the skillet in the oven and bake for 15-20 minutes, or until the yogurt topping is set and lightly golden.
Remove from the oven, garnish with fresh chopped parsley, and let sit for 5 minutes before serving.