01 - In a mixing bowl, combine plain yogurt, olive oil, minced garlic, ground cumin, ground coriander, smoked paprika, turmeric, cinnamon, salt, black pepper, and lemon juice. 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 and lightly charred on the edges. Transfer to a plate and let rest briefly.
03 - While the chicken rests, whisk together mayonnaise, Greek yogurt, minced garlic, lemon juice, and salt in a small bowl until smooth and well combined. Set aside.
04 - Warm each flatbread or pita in a dry skillet over medium heat for about 30 seconds per side, until pliable and lightly toasted.
05 - Spread a generous layer of garlic sauce across the center of each warmed flatbread. Layer with 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 up tightly to enclose the filling. Slice each wrap in half on the diagonal and serve immediately while warm.