Drizzle 2 slices of ciabatta (or 2 split rolls) with olive oil and vinegar. Layer on the proscuitto, soppressata, red peppers, pepperoncini, and the Parmegiano. Season with salt and pepper. Sandwich with the remaining slices and press down gently but firmly.
Wrap sandwiches tightly with plastic film or wax paper if you are packing them, or serve immediately.