Make the Dressing In a small bowl, whisk together mayonnaise, parmesan, red wine vinegar, banana pepper juice, oregano, garlic powder, salt, and pepper. Taste it — the flavor should be bright and tangy. If it feels too creamy, add a splash more vinegar for balance.
Combine the Base In a large bowl, mix shredded rotisserie chicken, diced salami, pepperoni, tomatoes, red onion, banana peppers, and cheeses.
Add the Dressing Pour most of the dressing over the bowl and toss until everything is evenly coated. Add more dressing if needed to reach that luscious, creamy texture.
Chill and Serve Let it sit for at least 15 minutes before serving to let the flavors meld. If prepping ahead, store it in an airtight container in the fridge for up to 4 days.