Heat 1 tablespoon Olive Oil in 6-quart saucepot over medium-high heat and brown beef, drain. Remove beef and keep warm.
Add remaining 2 tablespoons Olive Oil to same saucepot and cook, onions, carrots, celery, thyme and bay leaves, stirring occasionally, until vegetables are tender, about 10 minutes. Return beef to saucepot and stir in broth and barley and bring to boil. Reduce heat to low and simmer uncovered, stirring occasionally, until beef is tender and broth is thickened, about 1 hour 15 minutes. Remove bay leaves. Season, if desired, with salt and black pepper. Garnish, if desired, with chopped flat-leaf parsley.
Recipe courtesy of Fabio Viviani, owner and Executive Chef of Cafe Firenze in Moorpark, California and Firenze Osteria Italian Restaurant and Martini Bar in Toluca Lake, California.