01 - Preheat oven to 325°F.
02 - Pat the beef chuck roast dry and season generously with salt and pepper on all sides.
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 from pot 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 more until fragrant.
05 - Stir in tomato paste, smoked paprika, brown sugar, cumin, and chili powder. Mix thoroughly to combine and toast the spices briefly.
06 - Return the beef to the pot. Pour in beef broth and barbecue sauce. Bring to a simmer, cover tightly with lid.
07 - Transfer covered pot to the oven. Cook for 3–3.5 hours until the beef is fork-tender and shreds easily with minimal resistance.
08 - Remove beef from cooking liquid. Using two forks, shred the meat into bite-sized pieces. Return shredded beef to the pot and stir thoroughly to coat in sauce.
09 - In a large bowl, combine shredded green cabbage, purple cabbage, and grated carrot. Add mayonnaise, apple cider vinegar, honey, salt, and pepper. Toss until evenly coated. Refrigerate until ready to serve.
10 - Slice slider buns in half. Pile warm pulled beef onto bottom buns, top generously with coleslaw, and add optional pickles, red onion, or jalapeños. Replace bun tops. Drizzle with additional barbecue sauce if desired. Serve immediately.