Make sandwiches out of the bread and mozzarella, leaving a little margin around the edges unfilled with cheese, and press the edges together with your fingers to help seal. (One of the advantages of soft white bread is that it easily smushed together.) Pour the milk in to 1 soup bowl, the flour into another, and beat the egg with salt and pepper in another. Warm the oil in the frying pan over medium heat. Dunk the sandwiches briefly, 1 by 1, in the milk, then dredge in the flour, then dip in the beaten egg. Fry in hot oil on each side until crisp and golden and remove to a paper towel. Cut in half and apply to face.