To start, cook the wild rice by combining it, along with 2 cups of water and half a teaspoon of salt in a small saucepan; bring to a boil then reduce the heat to a slow simmer, cover and simmer until the rice is tender and almost all the grains have popped open, about 25 to 30 minutes. Once the rice is cooked to your liking, drain excess water if any and set aside.
While the rice is cooking, heat a splash of olive oil in a large saucepan set over medium heat; to it, add the onion, garlic, celery, salt and black pepper and cook for 2-3 minutes, until softened, slightly colored and fragrant.
Add the cauliflower florets and continue cooking for another minute or 2, then add the 4 cups of water, Dijon mustard, onion powder and half of the chopped mushrooms.
Bring to the boil then reduce the heat to a simmer, cover loosely and simmer until the cauliflower is fork tender, about 5-7 minutes.
Ladle this mixture into your high speed blender and process on high until super smooth and silky in consistency. There's a very good chance that you will have to work in 2-3 batches.
Return the soup to the saucepan and to it, add the rest of the chopped mushrooms as well as the cooked wild rice. Bring back to a boil, then reduce the heat and simmer until the mushrooms are cooked, about 3-4 minutes.
Dilute the arrowroot flour (or starch) in 1/4 cup of water, then mix in almond milk and pour that into the soup. Stir well and bring back to the boil, then kill the heat and serve.
The original of this recipe, published in January of 2013, called for 1 cup of Greek yogurt mixed in with 2 tbsp of arrowroot flour diluted in 1 cup of water. To keep the soup vegan this time, the yogurt has been replaced with almond milk and the water reduced to 1/4 cup, to make up for the thinner consistency of the milk vs the yogurt.