In a large bowl, combine olive oil, cumin, paprika, turmeric, coriander, cinnamon, minced garlic, lemon juice, salt, and pepper. Add the chicken thighs or breasts, ensuring they are evenly coated with the marinade. Cover the bowl and refrigerate for at least 30 minutes, or up to overnight.

While the chicken marinates, heat your grill or a non-stick skillet over medium-high heat. Drizzle a small amount of oil on the cooking surface to prevent sticking. Allow to get hot for about 5 minutes.

Once your cooking surface is ready, place the marinated chicken onto it. Cook for 5-7 minutes on each side, or until the chicken is golden brown and reaches an internal temperature of 165°F (75°C).

While the chicken is cooking, prepare the garlic sauce by whisking together mayonnaise, minced garlic, a splash of lemon juice, and a pinch of salt. Adjust the seasoning to your taste.

Once the chicken is cooked, remove it from the grill or skillet and let it rest for about 5 minutes. After resting, slice the chicken into thin strips.

Serve your Chicken Shawarma warm in pita pockets or on a plate. Drizzle with the creamy garlic sauce and accompany with fresh vegetables or a side salad.