In a food processor, puree the smoked mozzarella and1/4 cup EVOO into a thick paste; season with pepper. Pull out a small amount ofthe bread from the top half of each roll and spread with the mozzarella mixture. Spread the chopped olives and giardiniera on the bottom half of each roll. Layer with the tomato, romaine and basil; drizzle with EVOO. Divide the ham, prosciutto and soppressata among the bottom roll halves; set the roll tops in place.
Press together slightly. Transfer, top side down, to the beeswax wrapper or wax paper. Roll up as tightly as possible. Refrigerate up to 2 hours. Cut each sandwich into 3 pieces; serve cool or at room temperature. Pack pickles and celery, if using, in separate sealed storage containers.
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