01 - Pat the chicken dry and season generously with salt and pepper. Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Sear the chicken for 2–3 minutes per side until a golden-brown crust forms. Remove the chicken from the skillet and set aside.
02 - In the same skillet, combine the Rebel Float Root Beer, ketchup, apple cider vinegar, light brown sugar, Worcestershire sauce, Dijon mustard, smoked paprika, garlic powder, and cayenne pepper (if using). Stir to combine and bring the mixture to a simmer.
03 - Return the seared chicken to the skillet with the simmering sauce. Reduce the heat to low, cover the skillet, and let the chicken simmer for 25–30 minutes, turning it halfway through, until it is fully cooked and tender.
04 - Remove the cooked chicken from the skillet and shred it using two forks. Return the shredded chicken to the skillet with the sauce, tossing to ensure it is well-coated. Simmer uncovered for an additional 5–10 minutes to allow the sauce to thicken.
05 - In a medium mixing bowl, combine the shredded cabbage and carrots. Add the mayonnaise, apple cider vinegar, sugar, salt, and pepper. Toss the ingredients together until the vegetables are evenly coated. Cover and refrigerate until ready to assemble.
06 - Lightly toast the slider buns, if desired. Generously pile the root beer BBQ pulled chicken onto the bottom half of each bun. Top the chicken with a substantial portion of the prepared slaw. Add pickle slices, if using, and cap with the top half of the bun. Serve immediately.