Shred the rotisserie chicken into bite-sized pieces. Chop the iceberg lettuce, black forest ham, provolone cheese, pepperoni, and soppressata into small, uniform pieces. Slice the banana peppers and red onion.

In a large mixing bowl, combine the shredded chicken, chopped vegetables, mayonnaise, red wine vinegar, and Italian seasoning. Fold together gently until well-coated.

Lay out tortillas, spoon a portion of filling into each, fold the bottom edge, tuck in the sides, and roll tightly.

Slice each wrap in half diagonally and serve immediately for the best flavor and crunch.