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1. Trim fat from meat. If necessary, cut meat to fit into a 3 1/2- or 4-quart slow cooker. In the cooker, combine onion and sweet pepper. Add meat; sprinkle with thyme and rosemary. Pour broth over meat.
2. Cover and cook on low-heat setting for 9 to 10 hours or on high-heat setting for 4 1/2 to 5 hours.
3. Meanwhile, for barbecue sauce, in a medium saucepan, combine vinegar, ketchup, brown sugar, honey, Worcestershire sauce, mustard, garlic, black pepper, and salt. Bring to boiling; reduce heat. Simmer, uncovered, for 20 to 25 minutes or until slightly thickened, stirring occasionally.
4. Transfer meat to a cutting board. Using two forks, pull meat apart into shreds, discarding fat. Strain vegetable mixture, discarding liquid. Return shredded meat and strained vegetables to cooker. Stir in barbecue sauce. If using high-heat setting, turn to low-heat setting Cover and cook for 1 hour.
5. To serve, spoon meat mixture onto bun bottoms. Top with coleslaw and pickles. Add bun tops.