In the slow cooker, combine the wild rice, diced onion, minced garlic, diced carrots, and diced celery.
Pour in the vegetable or chicken broth and stir well to combine.
Add the dried thyme, rosemary, salt, and black pepper; stir again.
Cover the slow cooker and set it on low for 6 hours or high for 3 hours.
About 30 minutes before serving, add the coconut milk or heavy cream and chopped spinach to the slow cooker. Stir to combine.
Before serving, add the lemon juice and taste; adjust seasoning if necessary.
Ladle the soup into bowls and enjoy hot.
For a vegetarian version, use vegetable broth and coconut milk.
Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat on the stove or in the microwave.