Rinse the wild rice under cold running water until the water runs clear. Let drain and transfer to a large slow cooker (5 or 6-quarts/4-6 litres).
Add onion, celery, carrots, and garlic to a food processor and pulse until very finely minced and transfer to slow cooker pot.
Add ⅔ of the mushrooms to food processor and pulse until finely chopped. Thinly slice the remaining mushrooms and add to the pot along with the finely chopped mushrooms.
Empty the cannellini beans and the liquid into a food processor and blend until smooth. Pour into the pot with bay leaf, garlic powder, and 6 cups of vegetable stock. Season with salt and black pepper to personal preference. Stir to combine all the ingredients.
Cover and cook on high for 3-4 hours, or low for 6-8 hours. Actual cooking time will vary depending on your slow cooker so check the rice for doneness after 2½ hours (if cooked on high) or 5½ hours (if cooked on low), and adjust time accordingly. The rice should be tender, but not mushy. Remove bay leaf when soup is cooked.
When ready to serve, temper the half and half (single cream) by stirring a few spoonfuls of hot stock into it to warm it through, then pour back into the pot and stir. This helps to prevent the cream from curdling.
Add chopped parsley, and if you feel it is needed, extra (hot) stock to achieve the desired consistency. Stir soup to combine thoroughly.
Ladel into warmed bowls and serve immediately - enjoy!