Step 1: In a large bowl, combine chicken strips with olive oil, lemon juice, minced garlic, cumin, paprika, turmeric, coriander, cayenne (if using), salt, and black pepper. Mix well to coat evenly.
Step 2: Cover the bowl and let the chicken marinate in the refrigerator for at least 30 minutes, or up to 4 hours for more flavor.
Step 3: While the chicken marinates, prepare the yogurt sauce by mixing Greek yogurt, chopped parsley, lemon juice, minced garlic, and salt in a small bowl. Refrigerate until ready to serve.
Step 4: Heat a large skillet or grill pan over medium-high heat. Add the marinated chicken in a single layer, cooking for 6-8 minutes per side until golden brown and cooked through.
Step 5: Remove the chicken from the heat and let it rest for a few minutes before slicing into smaller pieces if desired.
Step 6: Serve the chicken shawarma on warmed pita breads, topped with yogurt sauce, sliced tomatoes, cucumbers, red onions, and fresh greens.