Place the puff pastry on a work surface and spread the mustard over the top. Arrange the prosciutto or thinly sliced ham evenly over the mustard to cover all of the pastry, and then sprinkle with the Parmesan cheese. Lightly press the cheese into the prosciutto with a rolling pin.
Starting at a long edge, roll up the puff pastry jelly-roll-style just to the middle of the dough; then roll up the other side in the same fashion, making two rolls that meet in the center. Using a serrated knife, cut the rolls crosswise into 1/2-inch slices. You may chill the roll to firm it up before slicing if you'd like.
Place the slices on cookie sheets lined with parchment paper and press lightly with your hands to flatten. Refrigerate for 15 minutes.
Preheat oven to 400 F.
Whisk the egg and water together in a small bowl. Brush the top of each palmier with the egg mixture.
Bake the palmiers until puffed and lightly browned, about 10 minutes.