Use a glass to cut out 4 circles of equal size from the bread slices. The glass should have about the same diameter as the mozzarella. Drain the mozzarella, cut it in half and place one half between two slices of bread.
Flour the sandwiches well from all sides. Whisk the egg on a plate with milk, salt and pepper and dip the mozzarella sandwiches into it. Leave them on the plate for 5 minutes so that the liquid can soak into the bread.
Heat plenty of oil and fry the sandwiches until golden brown and crispy. The mozzarella should melt. Briefly place the sandwiches on some kitchen roll so that it absorbs the excess oil. Serve while still very hot with a green salad and fresh pesto or with currant jam.
If you are in the mood for hearty flavours, you can, for example as the Romans do, add an anchovy or a slice of ham between the mozzarella and the bread. We especially like mozzarella in carrozza with a dried tomato on top of the cheese.