Cook the noodles. In a large pot of salted water, cook the noodles according to package directions. For most noodles, this should be around 10 to 12 minutes. Drain them and rinse under cold water. Set them aside.
Prep the vegetables. While the noodles are cooking, wash and chop the celery, red pepper, red onion, and carrots. Make these into small, bite side pieces. Place them in a large mixing bowl and set them aside.
Mix the dressing. Next, in a medium sized bowl, whisk together the ingredients for the dressing. Give it a taste and adjust for seasoning as needed.
Combine and serve. Finally, it’s time to combine everything into a large bowl. Pour the dressing over top and mix. Give it a taste again and adjust for seasoning one final time. After chilling, you may need an additional spoonful of vegan mayo to make the dressing creamy again. Just add one spoonful and mix into the entire noodle salad. Enjoy!