For the bocconcini: Drain the bocconcini and pat dry with paper towels. Put on a paper towel-lined plate and allow to dry in the refrigerator for 2 hours. Put the flour in a medium bowl and season with salt and pepper, to taste. Put the eggs in a second medium bowl and the bread crumbs in a third medium bowl. Coat the bocconcini in flour and then dip into the eggs. Roll the bocconcini in the bread crumbs until coated. Dip the coated bocconcini again in the eggs and then coat with bread crumbs. Freeze the breaded bocconcini for 20 minutes.
In a large heavy-bottomed saucepan, pour in enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 375 degrees F (If you don't have a thermometer, a cube of bread will brown in about 1 to 2 minutes). In batches, fry the bocconcini until golden brown, about 15 to 20 seconds. Drain on paper towels.
Arrange the bocconcini on a platter and serve with your favorite tomato sauce.