Whisk together olive oil, red wine vinegar, oregano, basil, grated garlic, Dijon, lemon zest, salt, black pepper, and a pinch of red pepper flakes in a large measuring cup. Stir the diced red onion into the dressing and let it sit to lightly pickle while you prepare the pasta (10 minutes).
Bring a large pot of well-salted water to a rolling boil. Cook the rotini 1 minute less than package al dente time (about 8–9 minutes), so it keeps its bite in the salad. Drain and rinse briefly under cool water to stop cooking, then shake off excess water well.
In a big mixing bowl, combine the cooled pasta, cherry tomatoes, sliced olives, chopped pepperoncini, and mini pepperoni. Pour in half of the dressing (with the onions) and toss thoroughly to coat. Let stand 10 minutes to allow the pasta to absorb flavor.
Fold in the mini mozzarella and shaved Parmesan. Add most of the remaining dressing and toss gently so the cheese stays intact. Taste and adjust seasoning with a pinch more salt or pepper, if needed.
Chill for at least 30 minutes before serving (or cover and refrigerate up to 24 hours). Just before serving, give it a quick toss and add the last splash of dressing if the pasta has absorbed a lot.
Tip: If you like a touch more tang, add an extra teaspoon of red wine vinegar right before serving to brighten the flavors.