Put the chicken in a medium bowl, sprinkle with the light and dark soy sauces and toss well to coat. Sprinkle the cornstarch and reserved spice mixture over the chicken, toss well and set aside for 5 minutes while you prepare the garnishes and sauce.
Heat the wok over high heat until smoking, and then add the oil. Pour the chicken into the wok in a single layer and let it settle and begin to brown before stirring. Stir-fry using a spatula until just cooked through, about 4 minutes. Pour in the mirin and toss until the liquid evaporates. Remove from the heat.
To assemble, spread the Spicy Hoisin Mayo evenly over the top and bottom pita halves. Divide the warm chicken among the pitas and top each with a slice of tomato, some pickled cucumbers and a lettuce leaf. Position the top pita in place and serve immediately. Alternatively, you can create pita pockets by slicing off the top third of each pita, pulling them apart, and stuffing them with the chicken, Spicy Hoisin Mayo and vegetables.