Add both stocks; bring to boil. Reduce heat and simmer 20 minutes, skimming fat if you have added the bone. At this point I will simmer for a few hours.
Add barley, thyme and oregano.
Simmer until barley is tender, stirring occasionally, about 35 minutes. This can be made 1 day ahead.
Add beef to soup; simmer until just cooked, about 10 minutes.