Season the chicken: Pat the chicken dry. Sprinkle with salt, pepper, smoked paprika, garlic powder, and onion powder.
Mix the sauce: In a bowl, combine BBQ sauce, apple cider vinegar, Worcestershire, brown sugar or honey (if using), and chicken broth. Stir until smooth.
Choose your cooking method: Slow cooker: Add chicken and sauce.
Cook on Low 4–5 hours or High 2.5–3 hours until shreddable.
Instant Pot: Add chicken and sauce. Cook on High Pressure for 10 minutes (breasts) or 12 minutes (thighs), then 10-minute natural release.
Stovetop: Simmer chicken and sauce in a covered pot over low heat for 25–35 minutes, turning once or twice.
Shred the chicken: Transfer chicken to a cutting board and shred with two forks. Return to the pot and toss in the sauce.
If the sauce is thin, simmer uncovered for a few minutes to thicken.
Make the slaw: In a bowl, mix mayo, vinegar, sugar, salt, pepper, and celery seed. Toss with coleslaw mix until coated but still crisp.
Toast the buns: Melt butter in a skillet over medium heat. Place buns cut-side down and toast until golden for extra flavor and structure.
Assemble: Add a generous spoonful of BBQ chicken to each bun.
Top with slaw and pickles or jalapeños if you like. Close and press gently.
Serve: Keep a little extra BBQ sauce on the side for dipping. Serve warm.