Place the chicken breasts in a 3 quart saucepan and cover with 2 cups of chicken broth. Bring the pot to a boil and then cover pot and reduce the heat to low. Simmer the chicken until fully cooked, about 25 minutes. Thinly slice the chicken and set aside.
Prepare the sriracha mayonnaise by stirring together the mayonnaise, sriracha, and sugar.
Prepare the pickled vegetables, by mixing together the lime juice, fish sauce, red pepper flakes, and brown sugar. Add the carrots, radish, cucumber, red onion, and mint.
Melt the butter in the skillet, and brown the insides of the rolls.
To assemble the rolls: spread them with the sriracha mayonnaise, and cover with layers of chicken and pickled vegetables. Sprinkle some cilantro on each sandwich and serve.