Cook the wild rice according to package instructions. When it's ready, set it aside.
While the rice is cooking, bring a large pot of water to boil. Add the cauliflower florets and boil until fork tender, about 10 minutes. When it's ready, drain the water and set the cauliflower aside.
While the cauliflower boils, heat olive oil in a large pot over medium heat. Add the carrot, celery, onion, rosemary and thyme and sauté until the vegetables begin to soften. Stir occasionally. Add garlic and continue to sauté until garlic softens, about 1 minute.
Add the mushroom broth and water to the pot, increase the heat and bring to a boil. Once boiling, reduce heat to low, cover the pot and simmer for 10 minutes.
While the soup is simmering, add the cooked cauliflower to a high speed blender or food processor. Add the full can of coconut milk to the blender along with the salt. Blend until completely smooth and creamy.
Add the creamed cauliflower and cooked wild rice to the simmering soup pot. Stir until everything is well mixed. Increase heat to medium and simmer for an additional 5 minutes.
Season with more salt and pepper as desired. Serve warm.