Place chicken breasts in a single layer in the bottom of a large slow cooker. Add 2 cups water. Cover and cook on high 2 hours or on low 4 hours.
Prepare the bbq sauce. Whisk together all sauce ingredients in a medium sauce pan. Bring to a boil over medium heat, then reduce to a simmer then cover and cook 15 minutes. Cover and chill until ready to use.
Prepare the slaw. Toss together all slaw ingredients in a large bowl, mixing well to coat evenly. Cover and chill until ready to serve.
Minutes before serving, remove chicken breasts from slow cooker and place in a large bowl. Discard water from slow cooker and wipe out the slow cooker. Shred chicken with two forks OR place chicken in the bowl of a stand mixer fixed with a paddle attachment and churn on low speed for 2-3 minutes.
Return shredded chicken to slow cooker and add the bbq sauce, mixing to coat all the chicken. Cook another 30 minutes. Serve on burger buns and top with slaw. If desired, drizzle your favorite bottled or homemade bbq sauce over the chicken on the sandwiches for an extra-saucy sandwich!