Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
Roll out pizza dough into a large rectangle (about 12x15 inches).
Spread a thin layer of pizza sauce over the dough, leaving 1-inch edges.
Layer mozzarella, Parmesan, pepperoni, salami, and ham evenly over the dough.
Sprinkle with Italian seasoning and red pepper flakes (if using).
Carefully roll the dough tightly from the long side into a log shape. Pinch the seams and tuck the ends.
Place seam-side down on the baking sheet. Brush with beaten egg and olive oil for a golden crust.
Cut 3–4 slits on top to allow steam to escape.
Bake for 22–25 minutes, until golden brown and cheese is melted inside.
Let cool for 5 minutes before slicing. Serve warm with extra pizza sauce for dipping.