Place bay leaves, halved onion, garlic, thyme, and peppercorns in a large saucepan with 6 cups cold water and stock. Bring to boil on high.
Add beef to saucepan. Return to a boil, skimming any foam from the top. Cook, covered, on medium-low heat for 1 hour or until beef is just tender. Strain over a large heatproof bowl. Reserve beef and liquid together, and onion and garlic together. Discard remaining solids. Mash onion and garlic in a small bowl until smooth.
Heat oil in a large saucepan on medium- high. Add chopped celery. Cook for 2 minutes or until starting to soften. Add reserved liquid and beef, onion mixture, chopped sweet potato and rinsed barley. Bring to boil. Reduce heat to medium- low. Cook, covered, stirring occasionally, for 30 to 40 minutes or until barley is tender. Season with salt and pepper.
Stir in trimmed green beans. Cook for 5 minutes or until beans are just tender. 6. Serve topped with extra thyme.