Place water and 1 tablespoon oil in a large pot; follow directions on the box of pasta noodles. Cook until slightly underdone.
Drain and rinse gluten free pasta noodles over cold water then set aside.
Meanwhile prep veggies and place 2 tablespoon oil in a large heated stove top pan. Place diced peppers, zucchini, and broccoli in pan and saute for a few minutes. Add in onion, garlic, olives, tomatoes, and seasonings, Saute to your level of doneness; I like my pasta salad veggies slightly crunchy in this cold, pasta salad.
Once pasta and vegges are done combine in a large serving bowl and gently toss. Drizzle with dairy free Italian dressing and gently mix until everything is evenly coated.
Top with dairy free Parmesan cheese and serve immediately or cover and place in the refrigerator up to a few hours. This salad is best the day of.