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. Cut each sheet into 4 equal squares (total of 8 squares).
Place 4 squares on the prepared baking sheet. Spread a thin layer of Dijon mustard on each square.
Layer 2 slices of ham and 2 slices of cheddar cheese on top of the mustard on each square. Season with garlic powder, thyme, salt, and pepper.
Top each stack with another puff pastry square. Press the edges to seal, and use a fork to crimp the edges for a decorative touch.
Brush the tops of each pastry stack with the beaten egg to give them a golden color when baked.
Bake in the preheated oven for 15-20 minutes, or until the pastries are puffed and golden brown.
Remove from the oven and let cool for a few minutes. Garnish with chopped parsley before serving.