1. Pour the two broths into a soup pot or Dutch oven. Add 3 cups water and bring to a boil over high heat.
2. While the liquid is heating, slice the carrots, adding them to the pot as you slice. Peel and chop the onion, adding it to the pot as you chop. Add the beef and barley.
3. When the soup begins to boil, reduce the heat to medium-low. Simmer, covered, stirring occasionally to prevent sticking, until the vegetables and the barley are tender, about 45 minutes.