Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

Roll out the refrigerated pizza dough on a floured surface to a rectangle about ¼ inch thick. Slice into six equal portions.

In a large mixing bowl, combine diced ham, mozzarella, cheddar, mayonnaise, mustard, garlic powder, onion powder, and salt and pepper. Stir well.

Scoop filling onto one half of each dough rectangle, leaving a ½ inch border.

Fold the other half of the dough over the filling and seal the edges with a fork.

Brush the tops of each pocket with the beaten egg.

Bake the hot pockets for 15-18 minutes until golden brown.

Remove from the oven, brush with melted butter, and let cool slightly before serving.