Heat the olive oil over medium-high heat in a large saucepan and sauté the onion and carrots for 3 minutes, until slightly softened. Add the barley and sauté for 2 more minutes until the barley is nicely coated with the oil and toasty looking.
Add 2 cups of beef broth, 2 cups of brisket sauce (or 1 cup of sauce and 1 additional cup of beef broth), and 2 cups of water. Partially cover and bring to a simmer, then reduce the heat to medium-low and simmer for 30 to 35 minutes, until the barley is pretty tender.
Turn the heat to high, add the chopped brisket and any chopped cooked carrots or other vegetables that were swimming around in the sauce, and bring to a simmer, uncovered. Return the heat to medium-low and let it bubble gently away for 10 more minutes.
Serve, and if you want, add some fresh chopped parsley.
Notes
You can make this soup up to 4 days ahead of time and store in an airtight container in the refrigerator. Reheat the soup in the microwave, or over low heat in a pot on the stovetop.