Preheat the oven to 400 degrees F. Spray 2 baking sheets with nonstick spray.
On a lightly floured surface, roll out both halves of the dough to large rectangles, about 9 by 13 inches. Sprinkle each with the sweet peppers, garlic, and Italian seasoning, leaving a 1-inch border. Evenly distribute the ham, sopressata, salami, pepperoni, and mozzarella over each of the dough rectangles.
Using a pastry brush, paint the border of 1 long edge on each piece of dough with the egg wash. Starting at the opposite long end without the egg wash, roll up each dough like a jellyroll. Repeat with the other dough. Place on the prepared baking sheets and brush the tops with olive oil. Sprinkle with smoked salt, if desired. Place a few slits in the top of the dough for venting. Bake until nearly completely golden brown and starting to crisp, about 25 minutes.
Remove from the oven and let cool for about 10 minutes. Slice thickly and serve with the warmed marinara.