Line a heavy large baking sheet with a silpat (nonstick baking mat) or parchment paper. Tear the dough along the perforations into strips. Using a pizza cutter or a large sharp knife, cut each dough strip in half lengthwise to form thin strips. Working with 1 dough strip at a time, roll each dough strip in the Parmesan cheese and twist. Transfer the dough strips to the prepared baking sheets.
Bake until the breadsticks are golden brown and crisp, about 20 minutes. Cool the breadsticks completely on the baking sheet.
Before serving, wrap 1 slice of prosciutto around each cooled breadstick. Arrange the prosciutto-wrapped breadsticks on a platter.