Preheat oven to 350°F. Line a large baking sheet with parchment paper or foil.
Unroll dough and place on work surface. Being careful not to tear dough, stretch with hands to a 16-by-9-inch rectangle. Layer ingredients down length of dough, in the center, in following order (overlapping as necessary): half of mozzarella, pepperoni, ham, peppers, green beans and soppressata. Finish with remaining mozzarella. Sprinkle oregano on cheese.
Bring long edges of dough over filling and position so edges overlap in center. Trim ends with a knife and pinch to seal edges. Transfer to prepared baking sheet and brush with oil. Cut 6 little slits on top with a small knife for ventilation.
Bake until puffed and evenly golden brown, 35 to 40 minutes. Let cool for 5 to 10 minutes. Before serving, trim a tiny slice from each end and discard. Cut stromboli into 4 equal portions.