In a large, heavy based stockpot heat half of the olive oil. Add the beef and cook until browned all over. Transfer to a plate and set aside.
Heat the remaining olive oil over medium heat. Add the onion and cook for 2 minutes, then stir in the carrot and celery for 5 minutes or until the onion is soft. Stir in the bay leaves, thyme, tomato paste and peppercorns. Cook for 2 minutes, then return the beef to the pan.
Pour the cold water over the beef and vegetables. Cover and bring to the boil, then reduce heat to low and simmer for 2 hours. Stir the bollito di carne occasionally, skimming any scum that rises to the surface.
Remove the stockpot from the heat. Transfer the beef and carrots to a chopping board and finely chop. Strain the beef soup through a fine sieve into a clean saucepan, using the back of the ladle to extract as much flavour as possible. Season with salt to taste.
To serve, divide the meat and carrots among serving bowls. Ladle hot beef stock over the beef and carrots and serve immediately – buon appetito.
Note: The beef stock can be served with small pasta as a starter or refrigerated/ frozen for another meal.