In a large soup pot, combine brisket and beef stock and bring to a boil, uncovered.
As the soup heats, make a bouquet garni (see note): Bundle peppercorns, garlic and bay leaf in cheesecloth and tie with kitchen string. Add the bouquet garni to the pot, then cover and simmer for 2 hours. Skim the top of the soup occasionally as the liquid simmers.
Remove the bouquet garni. Add celery, carrots, onion, cabbage and barley. Add tomato sauce and simmer, covered, for 20 minutes. Add kidney beans. Cover and simmer 10 more minutes.
Remove large chunks of beef from soup. Using two forks, shred the beef and return to soup pot. Add salt and pepper, if necessary, then serve.
Note: A bouquet garni is a bunch of herbs, spices and vegetables used to flavor stocks, sauces and soups. Typically, the flavorings are bundled in a cheesecloth bag. They also can be bundled inside a coffee filter or in pieces of celery stalk tied together.
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