Season the chicken. Pat the chicken dry and sprinkle with salt, pepper, smoked paprika, garlic powder, and onion powder.
This quick rub builds flavor fast.
Start the sauce base. In a small skillet or saucepan, combine BBQ sauce, broth or water, and 1 teaspoon apple cider vinegar. Add brown sugar or honey if you like it sweeter. Stir and bring to a gentle simmer over medium heat.
Simmer the chicken. Nestle the seasoned chicken into the sauce.
Reduce heat to low, cover, and cook for 12–15 minutes, turning once, until the chicken is cooked through and easily shreds with a fork. If the sauce gets too thick, splash in a tablespoon of water.
Shred and reduce. Transfer the chicken to a cutting board and shred with two forks. Return it to the pan and toss to coat.
Let it simmer uncovered for 2–3 minutes to thicken and cling to the meat. Taste and adjust seasoning—more vinegar for tang, more BBQ for sauciness, a pinch of salt if needed.
Make the slaw. In a bowl, stir together mayonnaise, mustard, 1 teaspoon apple cider vinegar, sugar (if using), celery seed, salt, and pepper. Add the coleslaw mix and toss until lightly coated.
You want it crisp, not soupy.
Toast the buns. Split the slider rolls and spread cut sides with butter. Toast in a skillet over medium heat until golden. This keeps them from getting soggy and adds a little crunch.
Assemble. Pile the BBQ pulled chicken onto the bottom buns.
Top with a mound of slaw and a few pickle slices if you like. Cap with the top buns and press gently.
Serve hot. These are best right away, while the buns are warm and the slaw is cold and crisp.