Drizzle the olive oil in a large pot over medium-high heat. Saute the yellow onion, carrots, and celery ribs until they start to soften, about 5 minutes.
Add the dried thyme and garlic cloves and stir briefly. Then, add in 8 ounces of chopped mushrooms and stir again.
Place the wild rice in a fine mesh strainer and rinse it under running water. Drain well, then add it to the pot and cover with 6 cups of water. Increase the heat to high so the water will start heating as fast as possible. Next, add in the chicken thighs, 2 teaspoons of fine sea salt, and 1 teaspoon of ground black pepper.
Once the liquid is boiling, cover the pot with a lid, lower the heat to a gentle simmer and cook for 50 minutes. You'll know the rice is done when it splits and has a chewy texture. (It shouldn't be crunchy when you test it.) If the rice isn't tender yet, cover the pot and cook for 5 to 10 more minutes.
Use tongs to carefully transfer the chicken breasts to a cutting board, then use two forks to shred the chicken. Transfer it back to the soup, stir in the coconut milk, and adjust the seasoning, as needed. I usually add salt a ½ teaspoon at a time, until the broth is very flavorful. (I typically add 1 extra teaspoon in total, but this will vary based on the type of salt you use and your taste buds.)
Serve warm right away. Leftovers can be stored in an airtight container in the fridge for up to 4 days, or you can freeze it for up to 3 months.
Notes
Nutrition information is for roughly 1 1/2 cups of soup, assuming you get 9 cups total from this recipe. This will vary based on the size of your veggies, and is just an estimate, not a guarantee. Prefer to use chicken breasts? You can cook these whole for about 25 minutes in the soup, or until the center reaches an internal temperature of 165ºF. As soon as they are cooked, use tongs to remove them from the soup and let them rest on the cutting board until the rice is tender. This way they won't dry out from over-cooking. Thickening Option: When the chicken is removed from the soup, you can transfer up to 3 cups of soup to a blender, add the coconut milk, and blend until smooth. Then pour this mixture back into the soup pot for a creamier, thicker texture.