Bring 4 quarts of water to a boil. Add 1 tablespoon sea salt and 1 pound pasta. Cook until al dente according to package instructions (about 12 minutes). Drain pasta and rinse under cold water to stop the cooking process.
In a large bowl, combine cooked pasta, bell pepper, zucchini, cherry tomatoes, green onions, pepperoncini, and olives (if using). Toss to combine.
Add grated Parmesan, mozzarella balls, and chopped parsley/basil to the bowl. Gently mix to incorporate all ingredients.
In a small bowl, whisk vinegar, 1/2 teaspoon black pepper, and a pinch of salt to make the dressing. Toss the dressing with the salad until well coated.
Chill the salad for at least 1 hour before serving to allow flavors to meld.