01 - Combine salt, pepper, paprika, garlic powder, onion powder, thyme, and brown sugar in a small bowl. Rub the spice mixture evenly over the entire surface of the trimmed beef brisket.
02 - Whisk together beef broth, Worcestershire sauce, apple cider vinegar, and Dijon mustard in a separate bowl. Pour the mixture over the seasoned brisket in the slow cooker.
03 - Cover the slow cooker and cook on low heat for 8 hours until the brisket becomes fork-tender and easily shreds apart.
04 - Transfer the cooked brisket to a cutting board. Use two forks to shred the meat, removing any excess fat. Skim the fat from the cooking juices, then return the shredded meat to the juices to maintain moisture.
05 - In a small bowl, whisk together mayonnaise, apple cider vinegar, Dijon mustard, sugar, salt, and pepper until smooth and well combined.
06 - Combine green cabbage, red cabbage, grated carrot, and parsley in a large bowl. Pour the dressing over the vegetable mixture and toss thoroughly to coat. Refrigerate until serving time.
07 - Brush the cut sides of slider buns with melted butter if desired. Lightly toast them in a skillet or oven until golden brown.
08 - Pile shredded brisket onto the bottom half of each bun. Top with a generous amount of coleslaw and add pickle slices if using. Place the top bun and serve immediately.