For the spice mix, put the peppercorns, paprika, salt, garlic powder, onion powder, coriander seeds, brown sugar, and cayenne pepper in a mortar. Then crush them using a pestle until a fine consistency is achieved (it doesn’t have to be perfect; some smaller lumps are okay). Alternatively, you can use a spice grinder.
For the chicken, lay the chicken out in a single layer and generously sprinkle 3 tablespoons or so of the spice mix over them. Use your fingers to massage the spices into the chicken. Alternatively, you can mix 3 tablespoons of spice mix with the olive oil, if using, and brush the mixture over the chicken pieces.
Using metal or pre-soaked wooden skewers, carefully skewer the marinated chicken pieces. At this stage, you can cover the skewers and store them in the fridge for a couple of hours for the flavors to develop further.
Place the skewers on a hot grill (or you can use a griddle). Keep turning them over every couple of minutes so that they cook evenly on all sides. The total cooking time should take 10 to 15 minutes. If you don’t have a grill, you can set your oven to broil and place the skewers on a baking sheet in the oven, turning after a few minutes, and checking to make sure they don’t burn. The chicken is cooked when its internal temperature is 165 degrees F.
For serving, brown the pita bread on the grill for 1 to 2 minutes, turning them over halfway.
Carefully remove the pita and spread about 1 tablespoon of hummus inside each one, then add a couple of tablespoons of the pickled cabbage. Use a fork to carefully push the pargiyot off the skewer and into the pita.
Drizzle the chicken with some tahini sauce and serve.