Cook pasta according to package directions until al dente. Drain and rinse under cold water to stop the cooking, then let it drain completely.
In a large bowl, whisk together mayonnaise, Greek yogurt, red wine vinegar, pepperoncini juice, Italian seasoning, garlic powder, onion powder, parmesan cheese, salt, and black pepper until smooth and creamy.
Add cooled pasta, ham, salami, pepperoni, cherry tomatoes, banana peppers, red onion, mozzarella balls, and shredded parmesan to the bowl and toss until everything is well coated. Cover and chill for at least 30 minutes to let the flavors blend.
Right before serving, gently fold in the shredded romaine or iceberg lettuce to keep it crisp. Taste and adjust the seasoning as needed, adding more pepperoncini juice, salt, or black pepper to taste. If you prefer a creamier pasta salad, stir in a little more mayo, sour cream, or Greek yogurt until you reach your desired consistency.