Preheat the oven to 375°F. Line a baking sheet with parchment paper.
On a lightly floured sheet of parchment paper, gently roll the puff pastry into a larger rectangle, about ⅛-inch thick. Trim the edges to create a clean rectangle.
Arrange the prosciutto evenly over one half of the pastry. Generously grate Parmigiano Reggiano over the prosciutto and season with freshly ground black pepper.
Fold the uncovered half of the pastry over the filling like a book. Gently press to flatten and seal.
Using a sharp knife or pizza wheel, cut the pastry into strips about ½ inch wide. Twist each strip several times and arrange on the prepared baking sheet, leaving about 1 inch between each one.
Refrigerate the baking sheet for 10 minutes to allow the pastry to firm up.
Whisk together the egg yolk and water, then lightly brush each grissino with the egg wash.
Bake for 15–18 minutes, or until deeply golden, puffed, and crisp.