Toss the onion and pepper into a slow cooker. Trip the fat from the pork and sprinkle with thyme, rosemary, salt and pepper. Nestle the pork into the crock pot on top of the veggies. Add the broth and cook on low for 9 to 10 hours, or until the pork shreds easily with a fork.
Carefully, place the pork and veggies in a bowl and drain the slow cooker of any liquid. Return the pork and vegetables to the slow cooker and shred the meet into bite sized chunks with a fork.
Meanwhile, make the barbecue sauce. Whisk the vinegar, ketchup, brown sugar, honey, Worcestershire sauce and mustard in a pan over medium-high heat. Season with ½ teas pepper and ¼ teas salt. Stirring, bring to a boil. Reduce heat and simmer for 20 to 25 minutes, until sauce is thickened and evenly coats the back of a spoon.
Toss the shredded pork and veggies with the balsamic honey sauce and let heat through for 1 hour longer on low.
When ready to serve, toast the buns and pile high the pulled pork. Top with crunchy slaw and a pickle. Serve.