Begin by preparing the chicken. In a large bowl, combine olive oil, cumin, paprika, allspice, cayenne pepper, garlic powder, coriander, salt, and pepper. Add the chicken thighs and coat them evenly with the spice mixture. Let the chicken marinate for at least 10 minutes, or for best results, cover and refrigerate for a couple of hours.
Heat a grill pan or a heavy skillet over medium heat. Once hot, place the marinated chicken thighs on the pan. Cook for about 7-10 minutes on each side, or until the chicken is thoroughly cooked and has a nice, charred exterior. Remove from heat and let it rest for a few minutes before slicing into strips.
While the chicken is cooking, prepare the salad. In a large bowl, combine the mixed salad greens, diced cucumber, halved cherry tomatoes, thinly sliced red onion, and chopped fresh parsley.
For the tahini dressing, whisk together tahini, lemon juice, minced garlic, and water in a small bowl until smooth. If the dressing is too thick, add a little more water to reach the desired consistency. Season with salt to taste.
Assemble the salad bowls by dividing the salad greens mixture among four bowls. Top with sliced chicken shawarma.
Drizzle the tahini dressing over each salad bowl just before serving.