01 - Preheat oven to 300°F.
02 - Pat the brisket dry and rub generously with smoked paprika, chili powder, cumin, salt, and pepper on all sides.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear brisket on all sides until deeply browned, about 8 minutes total.
04 - Remove the brisket and set aside. Add sliced onion and minced garlic to the pot, sautéing for 2–3 minutes until softened and fragrant.
05 - Return the brisket to the pot. Pour in beef broth and barbecue sauce. Cover tightly with a heavy lid.
06 - Transfer the pot to the preheated oven. Cook for 4 hours, or until the brisket is fork-tender and easily shreds.
07 - In a large mixing bowl, combine green and red cabbage with grated carrot. Whisk together mayonnaise, apple cider vinegar, Dijon mustard, and sugar. Toss the dressing with the vegetables. Season with salt and pepper to taste. Refrigerate until serving.
08 - Remove the brisket from the cooking liquid and transfer to a cutting board. Shred the meat using two forks, discarding excess fat. 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. Place the bun tops on top.
10 - Arrange sliders on a platter and serve immediately, with extra barbecue sauce on the side for drizzling.