Muffuletta Potato Skins

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4 large russet potatoes

1/3 cup finely chopped green olives with pimentos

1/3 cup finely chopped giardiniera, plus 1 tablespoon brine

1 small stalk celery, finely chopped

1 small shallot, finely chopped

1 tablespoon chopped fresh parsley

Pinch of ground oregano

1 tablespoon extra-virgin olive oil

Kosher salt and freshly ground pepper

4 tablespoons unsalted butter, melted and cooled

4 slices mild provolone, cut into 4 strips each

4 slices hot soppressata, cut into strips

4 slices genoa salami, cut into strips

3 slices mortadella, halved and cut into strips

Sliced pickled pepperoncini, for garnish