01 - Place the chicken breasts or thighs in a large saucepan or Dutch oven. Add chicken broth, smoked paprika, garlic powder, onion powder, salt, and black pepper.
02 - Bring to a simmer over medium heat. Cover and cook for 20–25 minutes, or until the chicken is cooked through and tender.
03 - Transfer the chicken to a plate and let cool slightly. Shred with two forks.
04 - In the same pot, discard any excess liquid, then add the shredded chicken back. Pour in the barbecue sauce, apple cider vinegar, brown sugar, Worcestershire sauce, and hot sauce (if using). Stir well to coat. Simmer on low heat for 5–10 minutes until heated through.
05 - While the chicken simmers, make the slaw: In a large bowl, whisk together mayonnaise, apple cider vinegar, Dijon mustard, sugar, salt, and pepper. Add the cabbage and carrots; toss to combine.
06 - Toast the sandwich buns lightly, if desired.
07 - To assemble, pile the pulled chicken onto the bottom half of each bun, top with slaw and pickle slices (if using), then cover with the top bun.
08 - Serve immediately.