Place brisket in a Dutch oven; add water to cover. Bring to a boil and cover; reduce heat, and simmer for 3 hours or until brisket is tender. Remove brisket from pan, and strain broth.
Return brisket and strained broth to Dutch oven. Add next 5 ingredients. Bring to a boil and cover; reduce heat, and simmer 30 minutes. Add barley; cook an additional 30 minutes.
Remove brisket to a serving platter; slice thinly across the grain. Drain vegetable and barley mixture, discarding bay leaf, and serve with brisket.