Cook the tortellini: Follow the package instructions to cook the gluten-free tortellini. Drain and rinse with cold water to stop the cooking process. Let the tortellini cool completely.
Prepare the vegetables and herbs: While the tortellini cools, halve or quarter the cherry tomatoes, depending on their size. Chop the fresh mozzarella balls, if using. Dice the red onion and mince the fresh parsley and basil.
Assemble the salad: In a large bowl, combine the cooled tortellini, cherry tomatoes, mozzarella balls, red onion, parsley, basil, and oregano. Drizzle with olive oil and toss gently to coat all ingredients evenly.
Season and serve: Season the salad with salt and pepper to taste. Toss again and chill in the refrigerator for at least 30 minutes to allow the flavors to meld. Serve cold and enjoy!