On a small cutting board, lay down a piece of plastic wrap, about 2 feet long. Stack the provolone cheese in the center in a roughly 5-inch area. Layer the sopresetta on top of the provolone followed by layers of salami, basil leaves, prosciutto, and mozzarella. Wrap tightly in plastic wrap, place in refrigerator, a 1/2 hour, with a heavy plate on top to press mixture together.
In a large salad bowl, toss together lettuces, pepperoncini, peppadew and olives.
In a small bowl combine balsamic vinegar, oregano, parsley, thyme, garlic, salt and pepper. Slowly whisk in oil to incorporate.
Remove cheese and meat stack from refrigerator and slice it into 2 1/2-inch strips that are 1/4-inch thick. Add dressing to salad and toss. Decorate top with meat and cheese pressed slices. Garnish with Parmesan.