Fill a saucepan with cold water (about ¾ of the way up the pot's side). Add bay leaves, peppercorns, a few generous pinches of salt, and chicken bouillon, and stir well.
Add chicken breasts and cook over medium heat for 25 to 27 minutes or until the chicken reaches an internal temperature of 165ºF–if the water begins to boil, reduce the heat to low.
Transfer the chicken to a cutting board and shred it using two forks, or transfer it to a stand mixer fitted with a paddle attachment and shred it on speed 1. Once the chicken is fully shredded, add barbecue sauce, a pinch of salt, and ground black pepper. Stir until well combined, then set aside.