In a large bowl, whisk together plain Greek yogurt, olive oil, lemon juice, minced garlic, ground cumin, ground coriander, smoked paprika, ground turmeric, ground cinnamon, salt, and pepper until well combined. Add the chicken and coat thoroughly. Cover and refrigerate for at least 1 hour.

Preheat your grill to medium-high heat (about 400°F). Lightly oil the grill pan if using.

Remove the chicken from the marinade and grill each side for 5-7 minutes until charred and cooked through (internal temperature 165°F). Let rest for 5 minutes before slicing.

For the creamy garlic sauce, whisk mayonnaise, Greek yogurt, minced garlic, lemon juice, olive oil, and parsley until smooth. Adjust thickness with water if needed.

Assemble the shawarma by laying sliced chicken over flatbread or in bowls. Drizzle with creamy garlic sauce and add fresh vegetables.