Slice rolls lengthwise without cutting all the way through. Spread both sides of each roll with 1 Tbsp. mayonnaise.
Toss lettuce and onion with olive oil, vinegar and oregano in a large bowl.
Layer one side of rolls, alternating 1/4 each of salami and cheese slices. Top with dressed lettuce and onion. Season with salt and pepper. Fold sandwiches closed and secure with toothpicks.
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