In a small bowl, whisk together the olive oil, rice wine vinegar, lemon juice, garlic, salt, onion powder, oregano, basil, and red pepper flakes. Adjust seasoning to taste and set aside.
Cook the farfalle according to package directions. Drain in a colander, rinse with cold water to stop the cooking process and cool the pasta completely, then drain a second time to remove excess water.
Transfer the cooked pasta to a large bowl. Add the artichokes, black olives, Castelvetrano olives, peperoncini, garbanzo beans, and red onion. Add half the dressing and toss gently to coat.
Sprinkle with Parmesan and parsley, add the remaining dressing, and toss to combine. Serve at room temperature or refrigerate until ready to serve.