In a large ziplock bag, pour all of the marinade ingredients into the bag.  Close the bag tightly and shake to mix the marinade. Add the sliced chicken.  Massage the marinade into the chicken. Refrigerate and marinate the chicken at least 4 hours or up to 24 hours.  The longer the chicken marinates, the more flavorful it will be.

Next, pickle the vegetables.  In a small saucepan, bring the water, rice vinegar, sugar, salt, and chiles to a boil.  Stir to dissolve the sugar and salt completely. Remove from the heat and set aside to cool to room temperature.

In a glass or plastic bowl with a tightly fitting lid, layer the carrots, jalapenos, and cucumber.  Pour the pickling liquid over the vegetables. Cover tightly and chill for at least 1 hour or up to 3 days.

Preheat a grill or grill pan to medium heat.  Remove the chicken from the marinade and grill until just cooked through, about 2-3 minutes per side.  Transfer to a plate and set aside.

To assemble the sandwich, open and arrange the buns on a serving plate.

In a small bowl, whisk together the mayonnaise and Sriracha.  Slather the buns with the Sriacha mayo.

Arrange the chicken slices evenly on one side of the bread.  Spoon the pickled vegetables, draining on the side of the bowl, onto the chicken.  Top with 3 sprigs of cilantro on each sandwich.  

Slice each sandwich in half diagonally to serve.