- Place mesquite into the firebox of a 250°F smoker.
- Trim fat cap to ¼ inch. Place brisket into a large foil pouch and pour in vinegar mixture, Worcestershire sauce, and honey. Place pouch in smoker and cook for 6 hours, changing chunks as needed.
- Remove brisket from pouch, spread mustard evenly on it, and massage Rub into meat. Place brisket back into smoker and cook for 10 hours, changing chunks as needed.
- Separate brisket halves along fat line. Slice across the grain as thinly as humanly possible, chop roughly, and place serving portion in halved buns.
- Place some vinegar mixture into a squirt bottle and serve with sandwiches.