Cook the wild rice according to package directions, but remove from heat about 5 minutes early (it will finish cooking in the soup). Set aside.
Heat olive oil and butter in a large Dutch oven or heavy pot over medium-high heat until the butter is melted and slightly bubbling.
Add onions, carrots, and celery to the pot and sauté for 5-7 minutes until the vegetables begin to soften and the onions become translucent.
Incorporate the garlic and cook for another 30 seconds until fragrant, being careful not to let it burn.
Add the mushrooms and cook for 8-10 minutes, stirring occasionally but not constantly. Allow them to brown properly – this develops crucial flavor. They’ll release moisture and then start to caramelize.
Pour in the white wine (if using) and scrape up any browned bits from the bottom of the pot. Let it simmer until most of the liquid has evaporated, about 2 minutes.
Sprinkle the flour over the vegetable mixture and stir continuously for 1-2 minutes to cook out the raw flour taste and form a roux.
Gradually add the broth, stirring constantly to prevent lumps, then add bay leaves, thyme, and rosemary.
Bring the mixture to a simmer and add the partially cooked wild rice. Let it cook for about 15 minutes, or until the rice is tender but still has a pleasant chew.
Reduce heat to low and stir in the heavy cream and soy sauce, simmering gently for another 5 minutes. Be careful not to boil after adding the cream.
Taste and adjust the seasoning with salt and pepper. Remember that soy sauce adds saltiness, so taste before adding more salt.
Remove bay leaves, ladle into bowls, and garnish with fresh parsley before serving.