Add the wild rice, sliced mushrooms, diced onion, diced carrots, diced celery, and minced garlic to the slow cooker.
Pour in the vegetable broth and stir in the dried thyme, bay leaf, salt, and black pepper.
Cover and cook on low for 6 to 7 hours until the wild rice is tender and has absorbed some of the broth.
Remove the bay leaf and stir the soup before serving.
Ladle into bowls and top each serving with chopped fresh parsley.