Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
On a lightly floured surface, roll out each sheet of puff pastry to smooth out creases.
Spread a thin layer of Dijon mustard over each sheet of puff pastry, if using.
Layer the sliced ham evenly over the pastry, followed by the cheese. Sprinkle with dried parsley, salt, and pepper if desired.
Starting from one edge, carefully roll the pastry tightly into a log. Repeat with the second sheet.
Slice each log into 1-inch thick pinwheels and place them on the prepared baking sheet, cut side up.
Brush the tops of the pinwheels with the beaten egg to give them a golden color when baked.
Bake in the preheated oven for 15-20 minutes, or until the pinwheels are puffed and golden brown.
Allow to cool slightly before serving.