Fill a large pot with water and bring it to a boil. Add the refrigerated spinach and cheese tortellini and cook according to the package instructions—typically about 3 to 5 minutes until they float to the top and are tender.
Drain the tortellini using a colander and rinse them briefly under cold water to stop the cooking process and cool them down for the salad.
While your tortellini cools, halve the cherry tomatoes, dice the cucumber into small cubes, and slice the olives. Cube the Italian salami and drain the mozzarella cheese balls.
In your large mixing bowl, add the cooled tortellini, cherry tomatoes, cucumber, olives, mozzarella, and salami. Toss everything gently to mix the colors and ingredients evenly.
Pour in the Italian salad dressing and sprinkle the grated Parmesan cheese, sesame seeds, paprika, celery seed, and garlic powder over the salad. Using a spoon or spatula, toss everything gently but thoroughly until the dressing and spices coat every ingredient beautifully.
Cover the bowl with plastic wrap or a lid and refrigerate the salad for at least 30 minutes before serving. Give the salad a gentle toss one more time and serve chilled or at room temperature.