In a medium bowl, beat together cream cheese, Italian seasoning, and Parmesan cheese until smooth and well combined.
Spread the cream cheese mixture evenly across each tortilla, leaving about 1 inch at the edges.
Layer provolone cheese halves down the center of each tortilla, then add overlapping rows of ham, salami, and pepperoni.
Top with roasted red peppers and banana peppers if using, then scatter spinach or lettuce over the meats.
Starting from one edge, roll each tortilla tightly but gently to create a compact cylinder.
Wrap each roll individually in plastic wrap and refrigerate for at least 1 hour.
Using a sharp serrated knife, slice each roll into 12 pinwheels. Garnish with fresh parsley and serve.
