Preheat the oven to 350°F with a rack in the center position.
Make the shawarma. In a large bowl, combine the yogurt, cumin, cardamom, turmeric, cinnamon, and salt. Add the chicken to the marinade and toss until fully coated.
Spread 1 tablespoon of olive oil onto a large rimmed sheet pan. Arrange the coated chicken, onion, bell peppers, and peppadews on the baking sheet and drizzle with the remaining 1 tablespoon olive oil. Bake for about 20 minutes, or until the chicken is cooked through and the veggies are tender.
Meanwhile, make the tahini sauce. In a medium bowl, whisk together the tahini, garlic, olive oil, lemon juice, salt, and ⅔ cup water until smooth and combined. It will look like it’s separating a bit before it all comes together–just keep whisking.
Top the pitas with the chicken and veggie mixture. Serve topped with cucumbers, tomatoes, tahini sauce and parsley.
