In the bowl of a food processor, combine the olives and giardiniera. Pulse until pieces are approximately 1/4 inch in size.
Transfer the olive mixture to a bowl. Stir in the red wine vinegar and olive oil. Set aside. (Olive salad can be made up to 24 hours in advance.)
Split the bread in half lengthwise and spread the cut sides with the olive mixture.
Layer the soppressata on the bottom half of the roll followed by the capicola, then salami, the mortadella and provolone. Arrange the arugula and the peppers on top of the provolone. Place the top of the roll on the sandwich and wrap tightly with plastic wrap.
Transfer the sandwich to the refrigerator and allow to rest for 1 hour or overnight.
To serve, cut the sandwich into 4 equal wedges.
For best results, allow the sandwich to rest overnight.