Trim the pork shoulder and cube into large chunks. Transfer pork to a 2 gallon zip top storage bag. Add the jerk seasoning, seal the bag and massage the seasoning all over the pork. Refrigerate overnight.
The next day, place the pork in the slow cooker, place the lid on top and turn it onto high for 6 hours or low for 8-10 hours or until pork is very tender and falls apart easily.
Meanwhile make the coleslaw
Use a food processor or box grater to shred the cabbage and carrot. Mix in a large bowl and set aside. In a small bowl combine the mayonnaise, vinegar, celery seed, salt and pepper and whisk. Pour the dressing over the cabbage and toss with salad tongs. Refrigerate until ready to use.
Use a slotted spoon to remove the pork and transfer to a large bowl. Use a ladle to scoop the braising liquid into a large measuring cup.
Transfer the pork to a large bowl and use two forks to pull and shred the pork. Return the pork to the slow cooker and add half a cup of vegetable broth and stir. Taste for seasoning. If it needs more liquid you can add more vegetable broth to tone down the heat slightly, or use some of the braising liquid to kick it up even more. Pork should be moist and juicy, but not soupy.
To make the sandwiches, split the rolls in half, place a leaf of lettuce on the bottom bun followed by a scoop of jerk pork, a spoonful of coleslaw and a sprinkle of sprouts.
Avoid touching the jerk seasoning with your bare hands -- if you have any open cuts, it will sting and if it gets near your eyes, it will burn like the devil himself (take it from someone who knows).