To make the beef stock: in a medium-sized stockpot oven, place the beef bones, carrot, onion, and celery. Add water enough to cover, salt generously, and bring to a boil. Lower the heat and let the broth simmer for an hour. Conversely, use 8 cups good-quality beef stock.
After the stock has simmered for 1 hour, drain through a fine sieve, reserving the bones and vegetables. Set the reserved ingredients aside and return the strained stock to the stovetop. Using a slotted spoon, skim any extra fat from the top of the broth. Bring the broth back to a boil over medium heat and lower to a simmer to reduce.
Meanwhile, place the bread crumbs, grated pecorino, parsley, and meat in a mixing bowl. Salt and pepper the meat, using your hands to mix as you season so that the meat is seasoned throughout. Once the meat is well mixed, use your hands to form small meatballs, about the size of walnuts.
Using a slotted spoon, gently drop the meatballs into the gently simmering broth. Let the broth and meatballs cook until the broth is reduced by 1/3 and the meatballs are cooked through, about 1 hour.