Combine rice, chicken stock and butter in large pan. When chicken stock begins to boil, turn heat down low; stir rice once, then cover pan tightly and simmer until all liquid is absorbed, about 15 minutes. Rice should be soft and slightly sticky so that it will hold together.
Set aside rice to cool. Add egg yolks and parmesan cheese to cooled rice; stir well. Refrigerate while making the other parts of the recipe.
In a saucepan, heat extra virgin olive oil and sauté onions and celery until golden, about five minutes. Add meat and brown. Stir in tomato paste, water, salt and pepper. Cover and simmer about 20 minutes. Add peas and cook for five minutes longer.
Add enough extra virgin olive oil to a pan with high sides so that it is about two inches deep, then turn to medium-high heat. While extra virgin olive oil is heating, shape rice mixture into round balls, about 1/2 cup each. With your finger, make a hole in each rice ball. Add one tablespoon of the meat filling and the cheese cube and cover the holes with more rice. Dip rice balls in egg whites and roll in bread crumbs until thoroughly coated. Drop carefully into heated extra virgin olive oil, a few at a time, and fry until golden, turning around for about 3-4 minutes. Remove with a slotted spoon and drain on paper towel. Serve warm or at room temperature and with a side dish of tomato sauce.