Rub the pork shoulder generously with the spice rub.
Place the pork shoulder in a slow cooker. Add 1/2 cup of water or broth to the bottom of the slow cooker.
Cook on low for 8-10 hours, or on high for 4-6 hours, until the pork is very tender.
While pork is cooking, prepare the coleslaw: In a large bowl, combine shredded cabbage, carrot, mayonnaise, apple cider vinegar, Dijon mustard, and sugar. Mix well and refrigerate.
Once the pork is cooked, shred it with two forks.
In a bowl, whisk together all Sauce ingredients.
Pour the sauce over the shredded pork and toss to coat.
Assemble sliders by placing a portion of the pulled pork on each slider bun. Top with tangy coleslaw.
