In a large bowl, combine the cooked chicken, olive oil, cumin, coriander, paprika, garlic powder, onion powder, salt, black pepper, and cayenne pepper (if using). Mix well to coat the chicken evenly with the spices.
Heat a skillet over medium heat. Add the seasoned chicken and cook for about 5-7 minutes, stirring occasionally, until heated through and slightly crispy.
While the chicken is cooking, prepare the pita breads or sandwich rolls by slicing them open.
Once the chicken is ready, layer the Havarti cheese on the bottom of each pita or roll.
Spoon the warm chicken mixture over the cheese, then add the shredded lettuce, sliced tomato, and cucumber.
Drizzle tahini sauce or garlic sauce over the top, then close the sandwich.
If desired, grill the sandwich in the skillet for 2-3 minutes on each side until the bread is golden and the cheese is melted.