Place pork butt in a large freezer bag, add the dry rub and rub it all over the meat. Close up the bag and let sit in fridge for at least 1 hour or up to 48 hours.
Place pork butt in slow cooker and pour in enough water to come two thirds of the way up the meat. Cook on low for 8 – 10 hours or on high for 4 -5 hours.
Remove pork from slow cooker, and pour out the liquid. Keep the slow cooker on.
Shred the meat using two forks. Discard any skin, bones and chunks of fat. Return the meat to the slow cooker, add 1½ cups of barbeque sauce and heat until the sauce is hot. You can turn the slow cooker up to high to make this go faster.
Heat the remaining ½ cup barbeque sauce in a small pan if desired to serve along side.
While meat is heating make the polenta cakes and coleslaw.
Grilled Polenta Cakes
Mix the cornmeal and cheese. Heat the milk and butter in a small saucepan just until the butter melts. Pour the milk mixture into the cornmeal mixture and stir to combine. Season with salt and pepper.
Heat the olive oil over medium heat in a large skillet. Form the cornmeal mixture into 8 equal patties about 3 inches across. Fry the polenta cakes in batches until golden brown, 3 – 4 minutes on each side. Keep warm until ready to serve.
Coleslaw
If using whole cabbage, finely shred with a sharp knife and place in a large mixing bowl. Otherwise pour the bagged coleslaw mix into a large mixing bowl. Add the other ingredients and mix well. Taste for seasoning and adjust to your liking. Can be made several hours or even a day ahead. Keep refrigerated until ready to serve.
To assemble the whole dish, top polenta cakes with pulled pork and coleslaw. Pass extra sauce to be added as desired.