Shred lettuce and thinly slice red onion. Quarter cherry tomatoes and drain banana peppers.
Stack deli meat and cheese together, then chop into small bite-sized pieces.
Combine lettuce, red onion, tomatoes, banana peppers, chopped meat, chopped cheese, and parmesan in a large bowl. Toss to mix.
Whisk together mayonnaise, red wine vinegar, calabrian chili paste, garlic powder, oregano, salt, and pepper.
Pour 3/4 of dressing over salad and toss well. Add remaining dressing if desired.
Serve immediately or chill for 30 minutes before serving.