Trim fat from meat. If necessary, cut meat to fit a 4- to 5-quart slow cooker. Place onions and garlic in the cooker. Top with beef. In a medium bowl, combine broth, Worcestershire sauce, dry mustard, thyme, salt, and cayenne pepper. Pour over beef in cooker.
Cover and cook on low-heat setting for 11 to 12 hours or on high-heat setting for 5-1/2 to 6 hours. Remove beef and onion from cooker, reserving juices. Using two forks, shred beef, discarding any fat. Skim fat from juices. Add onion to beef; add enough juices to beef to moisten. Place 2-cup portions of beef in airtight containers and refrigerate for up to 3 days or freeze for up to 3 months. Makes 6 cups.