Place the roast in a 3 1/2 quart slow cooker, and add the pickled mixed vegetables, pepperoncini, Italian dressing mix and beef broth. Stir to blend, cover, and cook on LOW for 18 hours (yes, 18 hours – a light timer works well if you don’t want to stay up until midnight to turn it on).
To serve, remove roast from the slow cooker. Shred the beef with your fingers, using it and the au jus for sandwiches.
Serve the pickled mixed vegetables alongside the sandwich if desired, or just include them with the meat.