Cook the broken spaghetti in a large pot of salted boiling water according to package directions until al dente; drain in a colander and rinse with cold water to stop cooking.
Place the cooled spaghetti in a large mixing bowl.
Add the halved cherry tomatoes, diced cucumber, diced red bell pepper, diced red onion, and drained sliced black olives to the bowl with the pasta.
In a small bowl or measuring cup, whisk together the 16-ounce Italian dressing, grated Parmesan, sesame seeds, paprika, celery seed, and garlic powder until well combined.
Pour the dressing mixture over the pasta and vegetables and toss gently until everything is evenly coated.
Cover the salad and refrigerate for 3 hours or overnight to allow flavors to meld before serving.