01 - Preheat oven to 300°F.
02 - Pat the brisket dry with paper towels. Season generously on all sides with smoked paprika, chili powder, ground cumin, salt, and black pepper, rubbing the spices into the meat.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Add the seasoned brisket and sear on all sides until deeply browned, approximately 8 minutes total.
04 - Remove the brisket and set aside. Add sliced onion and minced garlic to the hot pot, sautéing for 2-3 minutes until softened and fragrant.
05 - Return the brisket to the pot. Pour in the beef broth and 1 cup of barbecue sauce. Cover the Dutch oven tightly with a heavy lid.
06 - Transfer the covered pot to the preheated oven. Braise for 4 hours, or until the brisket is fork-tender and easily shreds.
07 - While the brisket cooks, combine the shredded green and red cabbage, grated carrot, mayonnaise, apple cider vinegar, Dijon mustard, and sugar in a large bowl. Season with salt and pepper to taste. Mix thoroughly until all vegetables are evenly coated. Refrigerate until ready to serve.
08 - Once the brisket is finished cooking, transfer it to a cutting board. Using two forks, shred the meat into bite-sized pieces. Toss with some of the reserved cooking juices and additional barbecue sauce if desired.
09 - Layer a generous portion of shredded brisket onto the bottom half of each slider bun. Top with a spoonful of coleslaw and 1-2 pickle slices. Close with the top bun.
10 - Arrange sliders on a serving platter and serve immediately with extra barbecue sauce on the side for dipping.