First remove any excess fat from the meat. Place the trimmed meat in the crock pot, cutting to fit if necessary. Add in the onion and pepper, and sprinkle the vegetables and meat with the thyme and rosemary. Pour broth over the meat.

Cover and cook on low for 9 to 10 hours or on high for 4 1/2 to 5 hours.

Meanwhile, we’ll be making the bbq sauce. Combine vinegar, ketchup, brown sugar, honey, Worcestershire sauce, mustard, garlic, black pepper, and salt in a medium sauce pan. Bring to a boil, then reduce heat to a simmer. Let the sauce simmer, uncovered, for 20 to 25 minutes, or until slightly thickened, while stirring occasionally.

Transfer meat to a cutting board. Use two forks to pull meat apart into shreds, discarding any fat, or use a stand mixer to do the job for you. Strain the peppers and onions and discard the liquid. Return shredded meat and vegetables to the crock pot. Stir in barbecue sauce until fully incorporated. Cover and cook for 1 more hour on low.