Inspired by the traditional Cajun sandwich on the same-named flat, round bread, this layered sub is perfect for feeding a big crowd (especially when prepared on a 24-inch hoagie roll). What sets this sub apart is the addition of giardineria - the pickled vegetable relish - which nods to this sandwich's Italian roots. Be sure to make it two hours ahead so the fillings have time to soften the bread ever so slightly.
Toss the giardineria, brine, green and kalamata olives, pepperoncini, onion, parlsey, olive oil and garlic together in a medium bowl. Cover and refrigerate for at least 1 hour; the mixture can be made up to a day ahead.
Slice the hoagie roll in half lengthwise, leaving the bottom half slightly thicker than the top half. Put both sides cut-side up and spread the mayonnaise evenly over the two. Top each side with the olive salad and drizzle with any remaining liquid from the bowl.
Shingle half of the provolone on the bottom bun, top with the mortadella (fold the meat as needed to fit), ham, and salami and finish with the remaining provolone. Carefully flip the top bun onto the bottom and press together. Wrap and refrigerate 2 hours. Slice into 12 to 14 small sandwiches, skewering each with a toothpick.