Heat a soup pot to medium. Add oil. Sauté onion, carrots, celery, garlic, and a pinch of salt for 3-5 minutes, until onion is translucent.
Add the chopped cauliflower and combine well with the sautéed vegetables.
Stir in 2 1/2 cups of water, the no chicken base, and granulated onion. Bring to a simmer and cook for about 5 minutes, until cauliflower is tender. Lower heat.
Carefully ladle 1 cup of the soup into a high-speed blender. Add 1/2 cup water and the raw cashews. Blend until perfectly smooth.
Pour the blended cashew mixture back into the pot. Add shredded vegan cheese, nutritional yeast, white miso paste, pepper, and cayenne (if using). Taste and adjust salt.
Cook on medium-low heat for about 10 more minutes, stirring occasionally, until the soup is extra creamy and heated through.