Rinse wild rice under cold running water until water is clear. Drain and transfer to a 5 or 6-quart slow cooker crock.
Add onion, celery, carrots, and garlic to a food processor and pulse until very finely minced and transfer to slow cooker crock.
Add 2/3 of the mushrooms to food processor and pulse until finely chopped. Thinly slice remaining mushrooms and add to slow cooker, along with the finely chopped mushrooms.
Add cannellini beans and a little water to food processor and puree until smooth. Pour into slow cooker crock with other ingredients. Add bay leaf, garlic powder, and 6 cups of vegetable stock. Season with salt and black pepper, to taste, and stir to thoroughly combine all ingredients.
Cover and cook on high for 3-4 hours or low for 6-8. Actual cooking time will vary, so check for doneness after 2½ hours (or 5½ hours on low) and adjust cook time accordingly. (Rice should be tender, but not mushy, when finished).
When cooking time is complete, remove bay leaf and discard. Add coconut milk, chopped parsley, and the remaining vegetable stock, if needed, to achieve the desired consistency.
Season with additional salt and black pepper, to taste, and stir to combine. Serve immediately and enjoy!