Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Roll out the pizza dough on a lightly floured surface to a rectangle about ¼-inch thick.
Sprinkle the Italian seasoning and garlic powder evenly over the rolled-out dough.
Layer the pepperoni, ham, and both types of cheese across the center of the dough, leaving about 1 inch of space around the edges.
Carefully fold the dough over the filling, starting at one long side and rolling it over to the other side. Pinch the edges to seal tightly.
Place the rolled Stromboli seam-side down on the prepared baking sheet. Cut a few slits on top of the dough to allow steam to escape.
Brush the beaten egg over the top of the Stromboli for a golden finish. Optionally, you can also brush the top with olive oil.
Bake in the preheated oven for 20-25 minutes, until the dough is golden brown and cooked through.
Remove from the oven and let it cool for a few minutes before slicing. Serve with marinara sauce for dipping.