Add oil to a large stockpot; heat over medium heat. Add diced celery, carrots, and onion. Cook until onions are translucent and veggies are soft. Add 1/4 teaspoon salt while cooking.
Stir cornstarch or flour into mirepoix. Add vegetable broth. Add salt to taste. Bring to a simmer over medium-high heat.
Add cauliflower, garbanzo beans, rice, 1 teaspoon salt, garlic powder, black pepper, and cayenne. Cover and continue simmering over low heat for 30-45 minutes or until cauliflower is tender.
Garnish with parsley, if desired.