Place 2 slices of mozzarella in between 2 slices of bread. If you're adding the puttanesca filling, combine those ingredients in a mortar and pestle or processor, and spread onto the bread before adding the cheese. Keep the sandwich whole or slice diagonally into triangles.
Prep the dredging station: place flour in one dish, and combine eggs and milk in another dish. Coat sandwiches in flour, shake off the excess, and soak in the egg mixture.
Heat oil in a pan and fry sandwiches on both sides, until golden brown and crispy.