In the bowl of a stand mixer, combine the water, yeast, sugar and salt. Let rest in a warm spot for about 10 minutes. Add 1 tablespoon Italian seasoning, olive oil, and 7 cups flour. Stir until well combined, about 3 to 4 minutes. Add as much of the remaining flour as needed to bring the dough together and form a soft and somewhat sticky dough. Knead on high for about 7 minutes. Transfer to a well-oiled bowl. Cover loosely with plastic wrap and a damp kitchen towel and let rest in a warm spot until doubled in size, about 2 hours.
Preheat oven to 425 degrees F and line a half sheet baking sheet with parchment paper and oil with olive oil.
Add the dough and press down into an even layer until the baking sheet is completely covered in pizza dough. Sprinkle with remaining Italian seasoning and parmesan cheese. Bake until golden brown and the middle is cooked through, about 15 to 20 minutes. Remove from oven and let cool completely. Slice into 6 large squares.
To assemble each sandwich, slice open the pizza crust square. In a small bowl, combine the olive oil and balsamic vinegar, and brush both sides with it. Top each with 2 slices mozzarella cheese, a handful of arugula (seasoned with a bit of salt and pepper), 1 slice ham, a few slices of salami, pepperoni and prosciutto. Sandwich together and then slice in half diagonally. Continue this process until all sandwiches are made. Place on a baking sheet and toast in the oven until warmed through and the cheese has melted, about 5 to 8 minutes. Serve immediately or at room temperature.