Place the chuck roast, broth, and salt in a pressure cooker or slow cooker. If using a pressure cooker, seal the lid and cook on high pressure for 45 minutes, then allow the pressure to release naturally. If using a slow cooker, cook on high for 4 hours or on low for 6 hours.
When the meat is tender, drain it almost completely, leaving about ¼ cup / 60 ml (2 fl oz) of the cooking liquid in the cooker.
Shred the meat directly in the pot with two forks.
Add the barbecue sauce to the shredded beef and toss until everything is well coated.
In a separate salad bowl, combine the coleslaw mix and dressing, and toss to coat.
Divide the BBQ beef and coleslaw among 4 dinner plates.
Serve the slaw on top of the beef and enjoy immediately.
