01 - In a mixing bowl, whisk together the plain yogurt, olive oil, minced garlic, ground cumin, ground coriander, smoked paprika, turmeric, cinnamon, salt, black pepper, and lemon juice until well combined. Add the chicken thigh strips and toss to coat evenly. Cover and refrigerate for at least 20 minutes, or up to overnight for deeper flavor penetration.
02 - Heat a large skillet or grill pan over medium-high heat. Remove the chicken from the marinade, allowing excess to drip off, and arrange in a single layer. Cook for 6 to 8 minutes per side until fully cooked through with a lightly charred exterior. Transfer to a plate and let rest briefly.
03 - In a small bowl, combine the mayonnaise, Greek yogurt, minced garlic, lemon juice, and salt. Whisk until smooth and creamy. Set aside.
04 - Warm the flatbreads or pita breads in a dry skillet over medium heat for about 30 seconds per side, or until pliable and lightly toasted.
05 - Spread a generous layer of garlic sauce across each warm flatbread. Layer on the cooked chicken strips, sliced tomato, red onion, cucumber strips, shredded lettuce, and chopped parsley.
06 - Fold in the sides of each flatbread and roll tightly into a wrap. Slice diagonally in half if desired and serve immediately.