Mince the boiled beef finely with a sharp knife or in a food processor.
Mix the minced beef with the bread, grated cheese, garlic, parsley, egg, salt and pepper until you have a smooth, homogeneous mass.
Take walnut sized pieces of the beef mixture and form them into round meatballs with the palms of your hands.
Place the flour, eggs and breadcrumbs into separate shallow bowls. Beat the egg. Gently roll each meatball in the flour, then the beaten egg, then finally the breadcrumbs. (You may need to re-shape them with your hands after breading them; the mixture is quite soft and can get misshapen as you roll them multiple times.)
In a large skillet, fry the meatballs in abundant oil, turning so they brown nicely all over.
Drain the polpette di bollito on paper towels and serve.