Place cashews in a bowl and cover with water. Soak at least 1 hour, up to 8 hours. Strain and set aside until ready to use.
Heat the avocado oil in a Dutch oven or large stock pot over medium-high. Add the onion and sauté, stirring occasionally, until onion begins turning brown, about 8 minutes.
Add the carrot, garlic, and mushrooms, and continue cooking, stirring occasionally, until mushrooms begin to deepen in color, about 5 minutes.
Add the wild rice, vegetable broth, sea salt, oregano, and nutritional yeast. Cover and bring to a full boil.
While the soup is coming to a boil, blend the coconut milk and cashews together in a small blender. Stir this mixture into the pot, replace the cover, and reduce heat to medium-low to cook at a simmer.
Continue cooking until soup has thickened and rice is cooked through, about 45 minutes. Taste soup for flavor and add more sea salt according to taste.
Scoop soup into bowls and serve!
