Shawarma is the name of the vertical spits of meat you see in Middle Eastern restaurants, normally eaten in pita bread with tabbouleh, cucumber, and tomato and topped with hummus or tahini. It’s the Middle Eastern take on fast food, and just as good made at home.
First make the marinade. Place the spices, garlic, lemon juice, and cilantro in a small blender or mortar and grind until smooth. Add 5 tablespoons of olive oil, along with a generous pinch of salt and pepper, and blend again to mix well. Transfer the marinade to a large dish. Add the chicken and rub in the marinade, making sure that all of the chicken is covered. Leave to marinate for up to 2 hours.
Preheat the oven to 400°F.
Heat a grill pan over medium heat. Remove the chicken from the marinade, shaking off any excess, and cook on the hot grill for 3–4 minutes on each side until slightly charred but not burnt. Transfer to a roasting pan and finish cooking in the oven for 5–8 minutes. Leave the chicken to rest.
Meanwhile, cook the tortillas in batches in a single layer on the cleaned, slightly oiled grill pan. Toast on each side for 2 minutes or until they are hot all the way through but still pliable. Keep warm.
Remove the chicken from the oven and slice into bite-sized chunks. Place some chicken on each warm wrap and sprinkle with scallions and shredded cabbage. Add mayonnaise and chile sauce to taste, then roll up the wraps and serve.