Arrange 4 slices of bread on a wooden board. Whisk the 2 eggs in a shallow dish. Prepare the bread crumbs on a piece of waxed paper. Cut the mozzarella in even thin slices.
Arrange the slices of mozzarella on the bread, sprinkle a little salt and pepper, then cover with the remaining four slices and press to close well.
Dip the sandwiches one by one in the egg mixture and then coat with the bread crumbs, making sure to shake the excess off.
Heat up a pan with the oil and then gently fry the sandwiches until golden brown and crunchy. The Mozzarella will be warm, almost melted and should form ribbons when pulled.