Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a medium bowl, mix the softened cream cheese, Dijon mustard, garlic powder, onion powder, salt, and pepper until well combined.
Roll out each sheet of puff pastry on a lightly floured surface to smooth out any creases.
Spread half of the cream cheese mixture evenly over each sheet of puff pastry.
Layer the sliced ham evenly over the cream cheese mixture, followed by an even layer of shredded cheddar cheese.
Starting from one edge, carefully roll the puff pastry tightly into a log shape. Repeat with the second sheet.
Slice each log into 1-inch thick pinwheels and place them on the prepared baking sheet.
Brush the tops of the pinwheels with the beaten egg to give them a golden color while baking.
Bake in the preheated oven for 15-20 minutes or until the pinwheels are puffed and golden brown.
Allow to cool slightly before serving.