Preheat the oven to 375 degrees F.
Sprinkle a clean dry work surface with flour. Roll the dough into a 10- by 14-inch rectangle, making sure not to flip the dough over, rotating by 90 degrees as needed. After rolling the dough, apply the egg whites to cover inner section (10- by 3-inch). Then add 1/4 cup mozzarella followed by both hams, another 1/4 cup cheese and then finish with the pepperoni. To finish stuffing, add the remaining cheese and drizzle with the sauce and herbs.
Next, brush the edges with some of the egg whites. Fold the bottom and top edges over the filling, and then fold the sides over twice, 1 inch at a time, resulting in a 6- by 14-inch tube. Brush the outside of the stromboli with the remaining egg whites, place on a sheet pan lined with parchment paper and bake until firm and golden brown, 15 to 18 minutes. Remove from the oven and let rest for 5 minutes. Cut into 5 to 6 portions and serve.