Tear the bread into bite-size pieces, place in a bowl, and drizzle with water or- use breadcrumbs or I like flavored croutons. Let soak until all liquid is absorbed.
In a large mixing bowl, combine the bread, onions, ground meat, one egg, mint, oregano, salt and pepper. Knead thoroughly until all ingredients are combined. If the mixture seems dry, add the other egg.
Take one tablespoon of the meat mixture at a time, shape into a small ball, and make an indentation in the center with your finger. Stuff each meatball with a little of the cubed cheese, and pat together to close completely.
Dredge the meatballs lightly in flour. Heat 2 inches of oil in a large skillet and fry the meatballs, turning, until golden brown on all sides. Remove, drain on paper towels and serve either hot or at room temperature.