Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
Unroll the puff pastry and spread Dijon mustard evenly over the surface.
Layer the ham slices evenly over the mustard.
Sprinkle shredded cheese evenly over the ham.
Roll up the pastry tightly from one edge to the other and slice into 1-inch pinwheels.
Place the pinwheels onto the prepared baking sheet, brush with egg wash, and bake for 15-18 minutes or until golden brown.
Garnish with parsley if desired, and serve warm.