01 - Preheat oven to 300°F. Pat the beef dry with paper towels and season with salt and pepper. Heat olive oil in a large Dutch oven over medium-high heat. Sear beef on all sides until browned, about 3-4 minutes per side. Remove and set aside.
02 - In the same pot, add onion and garlic. Sauté until softened, about 3 minutes. Add smoked paprika, brown sugar, cumin, and chili powder. Stir for 1 minute until fragrant.
03 - Return beef to the pot. Add beef broth, barbecue sauce, apple cider vinegar, and Worcestershire sauce. Bring to a simmer. Cover and transfer to the oven. Cook for 4 hours, or until beef is very tender and shreds easily.
04 - Remove beef from the pot. Shred using two forks, discarding excess fat. Return shredded beef to sauce and mix well. Keep warm until ready to serve.
05 - In a separate bowl, whisk together mayonnaise, Greek yogurt, apple cider vinegar, Dijon mustard, sugar, salt, and pepper until smooth.
06 - In a large bowl, combine shredded green cabbage, red cabbage, and carrots. Toss with dressing until evenly coated. Chill until ready to serve.
07 - Lightly toast the buns if desired. Pile generous portions of pulled beef onto the bottom half of each bun. Top with coleslaw. Drizzle with extra barbecue sauce if desired. Place the top bun on and serve immediately.