Place beef bones, carrots and celery in a large saucepan, cover with cold water. Bring to the boil, reduce heat and simmer covered for 1 hour to make beef stock. Skim the soup occasionally whilst it is cooking.
Meanwhile, preheat the oven to 180 C / Gas 4. Combine minced steak, lightly beaten egg and breadcrumbs in a bowl and season with salt and pepper. Take heaped teaspoonfuls of mixture and form into small balls. Coat a baking dish with oil and place meatballs in 1 layer.
Bake for 45 minutes, uncovered, turning occasionally. Remove, drain on absorbent paper.
Remove celery and carrots from stock and leave aside to cool. Remove bones from stock and strain stock into a large bowl then return to saucepan. Add the carrots and celery and the undrained mashed tomatoes. Bring to the boil, reduce heat and simmer for 15 minutes.
Place pasta in a saucepan of boiling water and par-cook for 10 minutes, then strain and rinse under cold water. Add to soup along with meatballs and cook for a further 10 minutes. Season with salt and pepper to taste and stir in chopped parsley.
The time required can be shortened with a ready made beef stock which I have done when time was short.