Fresh mozzarella rolls with spirals of prosciutto running through them are staples at every Italian-American deli. They are made by stretching the still-warm fresh mozzarella into a rectangle, covering the cheese with prosciutto and rolling the whole thing up into a neat loaf shape. As the mozzarella cools, it firms up and becomes compact and easy to slice. You can come close to this effect by following this procedure.
If you can buy fresh mozzarella ‘hot off the press,’ before it’s been refrigerated it will be easier to cut and fill. There are a lot of different fillings you can use in place of the prosciutto—olives, salami, fresh basil leaves or pesto.