Spread cream cheese on one side of a tortilla, all the way to the edges. Brush on dressing. Sprinkle with parmesan cheese. Cover one half with a single layer of salami and the other half with a single layer of pepperoni.
Add a layer of spinach of the entire tortilla and then sprinkle with pepperoncinis. Tightly roll up tortillas, doing your best to keep everything inside. Repeat process with remaining tortillas. Put in refrigerator to cool for at least 30 minutes.
When ready to serve, slice each tortilla roll into 8 equal piece, just less than an inch wide. You may need to tighten the roll for some of the outer pieces.