In a saucepan, over medium heat, combine the broth, beer and Worcestershire sauce and bring to a boil, then reduce heat to low.
Separate the slices of pastrami and drop each into the sauce, allowing the pastrami to heat through.
Place open buns on an ungreased cookie sheet or half-sheet. Place pastrami slices on one side of the bun, (reserving the cooking sauce). Place cheese on the opposite side of the bun. Broil for 1 to 2 minutes until cheese melts.
remove from broiler and spread mustard on pastrami.
Serve, cut into pieces and with bowls of the sauce for dipping.