If using store bought dough, remove it from the refrigerator about 30 minutes before rolling so it comes to room temperature and stretches easily. If making dough from scratch, prepare it according to your recipe and let it rest, covered, until easy to shape.
Preheat your oven to 400 degrees Fahrenheit. Line a large baking sheet with parchment paper, or lightly grease it with olive oil, and set aside.
Place the dough on a floured surface or parchment paper. Using a rolling pin, roll the dough into a rectangle roughly 10 by 14 inches, about a quarter inch thick, keeping the thickness even throughout.
Stir together the olive oil and minced garlic. Brush this mixture evenly over the entire surface of the dough, leaving a 1 inch border bare around the edges to help seal the roll later.
Working lengthwise, layer the salami evenly over the center two thirds of the dough. Add the pepperoni, then the capicola, then scatter the shredded mozzarella and lay the sliced provolone over the meats. Sprinkle the parmesan, oregano, and parsley evenly over the cheese layer.
Starting from one of the long sides, fold the bare 1 inch edge over the filling and roll the dough up tightly, jelly roll style, keeping the fillings tucked in. Pinch the seam closed and tuck the short ends underneath the loaf. Transfer to the prepared baking sheet, seam side down.
Beat the egg with a splash of water. Brush the egg wash evenly over the entire top and sides of the stromboli. Using a sharp knife, cut 3 to 4 diagonal slits across the top of the loaf to allow steam to escape while it bakes.
Bake the stromboli for 28 to 32 minutes, until the crust is deeply golden brown and the internal temperature of the filling reaches 165 degrees Fahrenheit. Let rest on a wire rack for at least 10 minutes before slicing into thick pieces and serving warm with marinara sauce on the side.