Marinate the Chicken: In a large bowl, combine sliced chicken thighs with salt, pepper, cumin, coriander, paprika, onion powder, turmeric, sugar, tomato paste, and olive oil. Mix well to evenly coat. Let marinate for at least 30 minutes, ideally overnight.
Cook the Chicken: Heat a large skillet over medium-high heat. Add marinated chicken and cook, stirring occasionally, until fully cooked and lightly charred in spots, about 8–12 minutes depending on thickness.
Make the Garlic Sauce: In a bowl, whisk together mayonnaise, yogurt, grated garlic, lemon juice, and parsley until smooth. Adjust seasoning to taste.
Prepare the Sumac Onions: In another bowl, mix sliced red onion with sumac, lemon juice, and parsley. Let sit for at least 10 minutes to soften and marinate.
Assemble the Wraps: Warm your lavash or flatbread. Spread a layer of garlic sauce (and harissa if using), then add lettuce, cooked chicken, sumac onions, pickles, tomatoes, and fries. Roll it up like a burrito or fold it like a gyro.
Serve and Enjoy: Enjoy your chicken shawarma wrap warm!