In a bowl or a liquid measuring cup, combine the mayonnaise, grated parmesan, apple cider vinegar, banana pepper juice, oregano, garlic powder, freshly cracked pepper, and salt. Mix until smooth and well combined.
Shred the rotisserie chicken and chop the turkey slices, turkey pepperoni, provolone cheese, and feta cheese into bite-sized pieces. Dice the grape tomatoes and thinly slice or dice the red onion.
In a large mixing bowl, toss together the shredded rotisserie chicken, diced deli meats, sliced red onion, grape tomatoes, banana peppers, and both cheeses.
Pour most of the dressing over the bowl of toppings and gently toss until well coated. Adjust the dressing to taste.
Transfer the salad into an airtight container and chill in the fridge for at least 30 minutes before serving.