Prep the produce: Clean and slice the mushrooms, dice the onion, carrots, and celery, and mince the garlic. Rinse the wild rice until the water runs mostly clear.
Sweat the aromatics: Heat the olive oil or butter in a large pot over medium heat.
Add onion, carrots, and celery. Cook, stirring often, until softened, about 6–8 minutes.
Add garlic and mushrooms: Stir in the garlic and mushrooms with a pinch of salt. Cook until the mushrooms release their liquid and begin to brown slightly, 7–10 minutes.
Season the base: Add thyme, bay leaf, soy sauce or tamari, salt, and pepper.
Cook 1 minute to bloom the spices.
Add rice and broth: Stir in the rinsed wild rice and pour in the broth. Bring to a boil, then reduce to a gentle simmer. Cover partially and cook until the rice is tender and split open, about 40–50 minutes.
Stir occasionally to prevent sticking.
Stir in beans: Add the cannellini beans and simmer 5 minutes to warm through. Taste and adjust salt and pepper.
Finish with creaminess: Reduce heat to low. Stir in the milk, half-and-half, or cashew cream.
Add the lemon juice for brightness. Don’t boil once the dairy is in; gentle heat keeps it smooth.
Serve: Remove the bay leaf. Ladle into bowls and top with chopped parsley if you like.
Serve with crusty bread or a simple salad.