Add the white wine vinegar, pepperoncini brine, kosher salt, Italian seasoning, black pepper, and minced garlic to a jar with a lid. Shake well to combine. Pour in the olive oil, close the lid, and shake again until everything is mixed. Set the dressing aside.
Bring a large pot of generously salted water to a boil. Add the farfalle pasta and cook according to the package directions.
During the last 3 minutes of the farfalle's cooking time, add the refrigerated cheese tortellini and green beans to the same pot. Continue cooking until the pasta is tender and the green beans are crisp-tender.
Drain the pasta, tortellini, and green beans in a colander. Rinse them thoroughly under cold water to stop the cooking process. Let everything drain well so extra water doesn't thin out the dressing.
In a large serving bowl, add the cherry tomatoes, pepperoni, red bell peppers, and chopped pepperoncini. Add the cooled pasta, tortellini, green beans, mozzarella pearls, and ½ teaspoon kosher salt.
Give the Italian dressing another good shake, then pour it over the salad. Gently toss everything together until the pasta and vegetables are evenly coated.
Sprinkle the fresh parsley over the top. Serve right away or refrigerate until you're ready to serve. If making it ahead, give it another toss before bringing it to the table.