Begin by preparing the eggplant puree. Preheat your oven to 400°F (200°C). Pierce the eggplants with a fork and place them on a baking sheet. Roast in the oven for 25-30 minutes or until the skin is charred and the interior is soft.
Once the eggplants are cool enough to handle, scoop out the flesh and place it into a food processor. Add the minced garlic, tahini, lemon juice, and olive oil. Blend until smooth, then season with salt to taste. Set aside.
In a mixing bowl, combine the ground lamb with cumin, smoked paprika, coriander, cayenne, salt, and pepper. Mix well.
Heat olive oil in a skillet over medium-high heat. Add the seasoned lamb and cook for 5-7 minutes or until the meat is browned and fully cooked. Break up the meat with a spoon as it cooks to ensure even browning.
For the mint yogurt, simply mix together Greek yogurt, chopped mint, lemon juice, and a pinch of salt in a small bowl. Refrigerate until ready to use.
Warm the flatbreads in the oven or on a skillet just before assembling.
To assemble, spread a generous layer of eggplant puree on each flatbread. Top with the cooked spiced lamb, followed by the sliced red onion, chopped parsley, and pomegranate seeds if using.
Drizzle with mint yogurt and serve immediately.