Slice the onion into ¼-inch rings and layer in the bottom of the crock pot. To the crock pot, add the beef broth, soy sauce, Worcestershire sauce, mustard, and garlic.
After trimming the meat of visible fat, salt and pepper both sides of the roast and place on top of the onions.
Cook on low 7-8 hours. Remove roast to a cutting board and shred meat using 2 forks and return meat to the crock pot to cook an additional few minutes, or up to 1 hour.
Preheat the broiler. Place the split sandwich rolls cut side up on a lined baking sheet and toast for 30-60 seconds or until the bread begins to brown. Top the bottom half with meat, onions, and a slice of cheese. Serve sandwiches with small bowls of jus for dipping.