Stir together the oil, vinegar and salt and pepper to taste.
Using a serrated knife, slice open the rolls. Drizzle half the dressing on the roll bottoms and sprinkle on the oregano. Divide the cold cuts, cheese, tomatoes, lettuce, onion and pepperoncini evenly among the bottom rolls. Top with the basil, if using. Drizzle the remaining dressing on the top halves of the rolls and place on top to make sandwiches. Wrap in wax paper. Slice in half and serve.