Prepare the dressing: In a small bowl, whisk together the olive oil, red wine vinegar, oregano, salt, and pepper.
Slice the rolls: Split the hoagie rolls lengthwise without cutting all the way through.
Layer the meats: Start with a layer of ham, then salami, then capicola.
Add the cheese: Place provolone slices over the meats.
Pile on the veggies: Add shredded lettuce, tomato slices, onion, and peppers.
Drizzle the dressing: Spoon the vinegar mixture evenly over the veggies.
Close and press: Fold the top of the roll over and gently press down.
Serve or wrap: Cut in half, wrap in parchment, and serve immediately or refrigerate for later.