Bring a large pot of generously salted water to a rolling boil. Add rotini and cook according to package directions, aiming for 1 minute less than recommended for al dente.
Drain pasta in a colander and immediately rinse under cold running water until cool to the touch. Shake well to remove excess water and let dry for a few minutes.
Combine olive oil, red wine vinegar, oregano, garlic powder, onion powder, sugar, and optional red pepper flakes in a small jar or bowl. Season with salt and pepper, then whisk or shake vigorously until emulsified.
Cut salami slices into halves or quarters. Halve cherry tomatoes, dice cucumber, slice olives, chop roasted red peppers, drain pepperoncini, finely dice red onion, and roughly chop parsley.
Transfer cooled pasta to a large mixing bowl. Add salami, tomatoes, cucumber, black olives, green olives, roasted red peppers, pepperoncini, and red onion. Pour about two-thirds of the dressing over the salad and toss until evenly coated.
Taste and adjust dressing, salt, or vinegar as needed. Add Parmesan cheese and fresh parsley, then toss gently once more to distribute throughout.
Cover tightly and refrigerate for at least 30 minutes, preferably 1 to 2 hours or overnight. Before serving, stir well and drizzle with extra olive oil or red wine vinegar if the salad looks dry.
Taste one final time and adjust seasoning, as cold temperatures dull flavors. Garnish with extra fresh parsley or Parmesan before serving.