Fill a large saucepan with water, season it generously with salt, and bring to a rolling boil. Add the spaghetti pieces and cook until tender yet firm, approximately 8 to 10 minutes. Drain thoroughly and rinse under cold water to halt the cooking process. Set aside to cool and drain completely.
Meanwhile, prepare the vegetables. Dice the cucumber, red and green bell peppers, and red onion. Halve the cherry tomatoes and drain the olives.
In a large mixing bowl, combine the cooled pasta with the chopped vegetables and sliced olives. Gently toss to distribute the ingredients evenly.
In a separate container, whisk together the Italian dressing with the Parmesan, sesame seeds, paprika, garlic powder, celery seed, and a touch of salt and pepper until well blended.
Pour the seasoned dressing over the pasta mixture. Toss thoroughly to coat all components. Cover the bowl and refrigerate for a minimum of 2 hours to allow the flavors to meld. For deeper flavor, let it chill overnight.
Before serving, stir the salad again to refresh the texture and taste. Adjust seasoning if necessary.