On a large cutting board, chop tomato, onion, ham, provolone, salami, soppressata, lettuce, red peppers, and peperoncini with a sharp knife, tossing as you go, until bite-sized pieces form.
In a large bowl, combine mayonnaise, pesto, vinegar, onion powder, and Italian seasoning; season with salt and pepper and stir to combine. Add chopped ham mixture and toss with a spatula or spoon until coated.
Distribute chopped mixture between rolls. Cut each roll in half to serve.
