**Sauté Vegetables:** Heat olive oil in a large pot over medium heat. Add the onion, garlic, carrots, and celery, and sauté for 5–7 minutes until softened.
**Add Mushrooms:** Stir in the mushrooms and cook for another 3 minutes, allowing them to release their moisture.
**Add Rice and Liquids:** Add the wild rice, vegetable broth, water, thyme, sage, black pepper, and salt. Stir to combine.
**Simmer:** Bring the soup to a boil, then reduce the heat to low. Cover and simmer for 40–50 minutes, or until the rice is tender.
**Add Cream and Greens:** Stir in the heavy cream (or coconut milk) and chopped spinach or kale. Cook for 5 minutes until the greens are wilted.
**Serve:** Ladle the soup into bowls and enjoy warm.