Place the rinsed wild rice, sliced mushrooms, diced onion, diced carrots, and minced garlic into the slow cooker.
Add the vegetable broth, dried thyme, and bay leaf. Stir once to combine the ingredients.
Cover and cook on low for 6 to 7 hours until the wild rice is tender and has absorbed most of the liquid.
Remove the bay leaf. Stir in the heavy cream and season with salt and black pepper.
Ladle the soup into bowls and top each serving with chopped fresh parsley.