Remove the mozzarella sticks from their wrappers. Place them on a wax-paper-lined platter and freeze for at least four hours and preferably overnight.
Preheat your oven to 400 degrees F. Line a rimmed baking sheet with parchment paper.
Wrap each mozzarella stick in a prosciutto slice, as shown in the video below. As you wrap it around, the edges of the prosciutto will stick to each other so that it’s fairly neatly wrapped. Prosciutto is sliced very thinly, so a few pieces might tear when you try to remove them from the package. Don't worry about it - the torn pieces are the chef's bonus. :) But you might want to get an extra package of prosciutto just in case.
Place the wrapped mozzarella sticks, seam side down, on the prepared baking sheet. Bake them until the cheese just starts to melt, about 5 minutes. Serve hot or at room temperature.