Coat the pork roast evenly with the pork rub, pressing the seasoning into the meat so it sticks well.
Place the seasoned pork roast in the slow cooker.
Pour the root beer, Dr Pepper, or chicken broth around the pork roast, avoiding pouring directly over the top.
Cover and cook on Low for about 8 hours until the pork becomes very tender and shreds easily.
Transfer the pork to a large bowl and add some of the cooking liquid if needed to keep the meat moist.
Shred the pork using two forks and mix with BBQ sauce. Serve on Hawaiian rolls or enjoy as desired.