Split each roll and scoop out inside, leaving a ½-inch shell.
Arrange lettuce in an even layer on a large cutting board or work surface. Top evenly with ham, salami, cheese, tomato, onion, and banana peppers. Using a large knife, chop through ingredients until mixture is evenly chopped and combined.
Whisk together mayonnaise, olive oil, vinegar, oregano, and black pepper in a small bowl. Pour over lettuce mixture; chop to combine. Spoon mixture into prepared rolls.
