Place stew meat in the bottom of a 4-quart or larger slow cooker.
Add barley, beef broth, water, thyme, marjoram, salt, and pepper. Stir once to combine.
Cover and cook on low for 7 1/2 to 8 hours, until beef is tender and barley is plump.
About 30 minutes before serving, stir in frozen mixed vegetables and switch slow cooker to high.
Taste and adjust seasoning before serving. Ladle into bowls and serve hot.
Notes
Use medium pearl barley, not quick barley, so it holds up during the long cook. Add frozen vegetables near the end so they stay bright and do not turn mushy. Taste before serving because barley absorbs salt as it cooks. The soup is even better the next day.