Slice the onion into ~¼-inch rounds. Keeping the rounds intact, place them in the bottom of the slow cooker. Add beef broth, soy sauce, Worcestershire sauce, mustard, and garlic to the slow cooker. Salt and pepper both sides of the roast and place on top of the onions. Cook on low 6-7 hours until beef is fall-apart tender.

Transfer the roast to a cutting board and shred using two forks. Remove the onions and set aside. Use a spoon (or fancy instrument if you have one) to remove the fat from the broth. Return the roast, juice, and onions to the slow cooker for up to an hour before serving.

Heat the broiler. Place the split sandwich rolls on a lined baking sheet and toast for 1 minute or just until the bread begins to brown. Remove the tops from the pan. Scoop the beef onto the bottom of the rolls and top with cheese. Return to the oven just until cheese is melted. Top with sandwich halves and serve with small bowls of jus.