Place dough in a large bowl. Cover with plastic wrap and let rise in a warm place until doubled, 45 minutes to 1 hour.
Roll dough into a 17x20-inch rectangle about 1/4-inch thick on a large piece of parchment paper. Brush olive oil over dough; sprinkle basil and oregano on top. Layer mortadella, provolone cheese, capicola ham, Genoa salami, tomatoes, and mushrooms over dough.
Roll dough lengthwise into a log. Brush the top with beaten egg; sprinkle sesame seeds on top. Transfer to a baking sheet. Cover with plastic wrap and let rise until puffy, about 30 minutes.
Preheat oven to 300 degrees F (150 degrees C).
Bake in the preheated oven until golden brown, about 45 minutes. Let cool for 5 minutes before slicing.