Start by preparing all your ingredients so assembly flows smoothly. Shred the chicken into bite-sized pieces and set aside. Cut the salami into 1/2-inch squares and dice the provolone into 1/4-inch cubes—I find cubing the cheese rather than slicing it helps it distribute more evenly throughout the salad. Halve the grape tomatoes lengthwise (this makes them easier to eat in each bite), thinly slice the red onion, and measure out the banana peppers. Have all these components ready in separate small bowls before you begin mixing.
In a medium mixing bowl, whisk together the mayonnaise, red wine vinegar, and banana pepper juice until smooth and well combined. This creates your flavor base. Add the oregano, garlic powder, salt, black pepper, and red pepper flakes, stirring until the spices are fully distributed and the dressing is evenly seasoned. I like to add the freshly grated parmesan at this point rather than at the end—it dissolves slightly into the dressing and creates a more cohesive, creamy texture throughout the entire salad rather than settling at the bottom.
In a large mixing bowl, combine the shredded chicken with the prepared salami, pepperoni, diced provolone, crumbled feta, halved tomatoes, banana peppers, and sliced red onion. Pour the Italian dressing from Step 2 over everything and toss gently but thoroughly to coat all components evenly. The key is using enough dressing to coat without making it soupy—the flavors meld beautifully as the ingredients marinate in the dressing for a few minutes.
Transfer the chicken salad to a serving bowl or platter. Serve immediately with your choice of accompaniments such as crackers, bread, chips, or fresh vegetables. The salad can also be made a few hours ahead and refrigerated—the flavors actually deepen as it sits—just give it a gentle stir before serving.