Combine olive oil, garlic, turmeric, cumin, black pepper, paprika, cinnamon, cardamom, and salt in a large bowl or Ziplock bag. Add chicken thighs and coat thoroughly. Let it marinate for at least 3 hours, or overnight for the best flavor.
You can grill, sear in a pan, or oven-roast the chicken. Make sure to cook until the internal temperature reaches 160°F. For extra color, broil the chicken for a few minutes at the end.
Whisk together yogurt, mayonnaise, grated garlic, za’atar, lemon juice, and salt in a small bowl. Chill in the fridge until ready to serve—it really brings the shawarma to life.
Slice the cooked chicken and arrange it on a platter. Serve warm with garlic white sauce on the side, pita bread, or over a salad.