Preheat the oven to 425º F.
On a lightly floured work surface, divide pizza dough half. Working with one piece at a time, roll the dough into a 9x12-inch rectangle. Spread ¼ cup pizza sauce over the dough, leaving a 1-inch border all the way around the dough. Carefully layer half of the pepperoni and half of the salami slices over the sauce. Sprinkle with half of the mozzarella and ½ teaspoon Italian seasoning.
Starting at one long edge, loosely roll the dough up like a jelly roll, tucking in the sides as you go. Place seam side down and to one side of a large baking sheet. Repeat the process with remaining dough, sauce, meats, cheese, and seasoning.
Brush strombolis with the egg. Using a sharp knife, cut several small slits on top of strombolis. Sprinkle with remaining ¼ teaspoon Italian seasoning.
Bake for 16 to 19 minutes or the crust is golden brown. Let cool for a few minutes before serving. Serve with extra pizza sauce.
