In a large bowl, whisk together the yogurt, olive oil, lemon juice, minced garlic, cumin, paprika, turmeric, coriander, cinnamon, salt, and black pepper until smooth and evenly spiced. The marinade should be thick enough to coat the chicken generously.
Add the chicken thighs to the marinade and turn until every piece is well coated. Cover and refrigerate for at least 2 hours, or overnight (up to 24 hours) for the deepest flavor. The yogurt tenderizes the meat while the spices penetrate.
While the chicken marinates, whisk together the mayonnaise, yogurt, lemon juice, grated garlic, and salt in a small bowl until creamy. Cover and refrigerate until serving — the flavor gets better as it sits and the garlic mellows.
Preheat the oven to 425°F (220°C). Line a rimmed baking sheet with foil and arrange the marinated chicken in a single layer, letting excess marinade drip off. Roast for 20–25 minutes until the chicken is cooked through (165°F / 74°C internal temperature) and the edges are charred in spots. For extra char, broil 2–3 minutes at the end.
Transfer the chicken to a cutting board and rest for 5 minutes so the juices redistribute. Slice thinly against the grain — thin slices are the shawarma signature and soak up the sauce beautifully.
Warm the pita breads directly over a gas flame for a few seconds per side, or in a hot dry skillet, until soft and puffy. Spread each pita generously with garlic sauce, pile on the sliced chicken, then add pickles, tomato slices, parsley, and a handful of hot fries. Roll up tightly and serve immediately.