Place roast in a 5-quart slow cooker. Stir together broth and next 4 ingredients and pour over roast. Cover and cook on high setting one hour; reduce heat to low setting and cook 9 hours.
Remove roast from slow cooker, reserving broth; shred roast with 2 forks. Place shredded meat evenly on hoagie buns and top with Swiss cheese. Serve with reserved broth for dipping.