Heat oil over medium-high heat. Add meat; sauté until well browned. Remove brisket to a plate. Add garlic and 1 cup of water to pot, scraping sides and bottom. Return meat to pot; add 6 cups water. Heat to boiling; reduce heat and simmer, covered, skimming the surface to remove excess fat, 1½ hours.
Place dried mushrooms in a mixing bowl. Cover with boiling water; let stand 30 minutes. Drain.
Discard garlic from pot; skim surface of any remaining fat. Add onion, carrots, parsnips, turnips, celery, mushrooms, tomatoes, both stocks, barley and thyme. Bring to boil; reduce heat and simmer, partially covered, until meat is tender, about 1½ hours.
to serve: remove meat and cut it into pieces. Return pieces to stew. Season with salt and pepper. Serves 6.