Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large bowl, combine the shredded chicken, ham, Swiss cheese, mozzarella cheese, garlic powder, onion powder, parsley, and black pepper. Mix well to combine.
Roll out the pizza dough on a lightly floured surface into a rectangle about 12x16 inches.
Spread the Dijon mustard evenly over the dough, leaving a 1-inch border around the edges.
Spoon the chicken and cheese mixture onto the dough, spreading it evenly over the mustard.
Starting from one long side, carefully roll the dough up tightly into a log. Pinch the edges to seal and tuck the ends under.
Place the stromboli seam-side down on the prepared baking sheet. Brush the top with the beaten egg and drizzle with olive oil.
Bake for 25-30 minutes, or until the stromboli is golden brown and cooked through.
Let it cool for 5-10 minutes before slicing. Serve warm.