01 - Preheat oven to 325°F.
02 - Pat the beef chuck roast dry with paper towels and season generously with salt and pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear the beef on all sides until deeply browned, about 2-3 minutes per side. Remove beef and set aside.
04 - Add sliced onion to the same pot and cook for 2-3 minutes until softened. Add minced garlic and cook for 1 minute until fragrant.
05 - Stir in tomato paste, smoked paprika, brown sugar, cumin, and chili powder. Mix well to combine and toast the spices for about 30 seconds.
06 - Return the beef to the pot. Pour in beef broth and barbecue sauce. Bring to a simmer, cover with a tight-fitting lid, and transfer to the oven.
07 - Braise for 3 to 3.5 hours, until the beef is fork-tender and shreds easily with minimal resistance.
08 - Remove the beef from the pot and shred using two forks. Mix the shredded beef back into the cooking juices until well coated.
09 - While the beef cooks, combine shredded green and purple cabbage, grated carrot, mayonnaise, apple cider vinegar, honey, salt, and pepper in a large bowl. Toss thoroughly and refrigerate until serving.
10 - Split the slider buns in half. Pile warm pulled beef onto the bottom buns, top generously with slaw, and add optional toppings such as pickles, red onion, or jalapeños. Drizzle with additional barbecue sauce if desired. Serve immediately.