Preheat your oven to 400°F (200°C).
Slice the eggplant in half lengthwise and score the flesh in a diamond pattern without cutting through the skin.
Brush the cut sides of the eggplant with olive oil and roast on a baking sheet for 20 minutes until the flesh is soft.
While the eggplant roasts, sauté the diced onion and minced garlic in a skillet over medium heat until fragrant.
Add the ground lamb to the skillet along with cumin, cinnamon, salt, and pepper, browning the meat until fully cooked.
Stir in the crushed tomatoes and simmer for 5 minutes until the liquid has slightly reduced.
Remove the eggplant from the oven and use a spoon to press down the center of the flesh to create a well.
Fill each eggplant half with the spiced lamb mixture.
In a small bowl, whisk together the Greek yogurt and the egg until smooth, then pour the mixture over the lamb filling.
Return the eggplant to the oven and bake for an additional 12-15 minutes until the yogurt topping is set and golden brown.
Garnish with freshly chopped parsley before serving.