Cook the wild rice according to the package directions. Drain any excess liquid and set aside.
Heat the butter and olive oil in a large Dutch oven over medium heat.
Add the onion, carrots, and celery. Cook for 7 to 8 minutes, stirring occasionally, until softened.
Stir in the garlic and cook for 30 seconds, until fragrant.
Add the mushrooms and cook for 12 to 15 minutes, stirring occasionally, until they release their moisture and become deeply browned.
Stir in the salt, pepper, thyme, rosemary, sage, and smoked paprika.
Pour in the white wine, if using, and cook for 2 to 3 minutes until nearly evaporated.
Sprinkle the flour over the vegetables and mushrooms. Stir continuously for 2 minutes to cook out the raw flour taste.
Gradually whisk in the broth until smooth. Add the bay leaf.
Bring the soup to a gentle simmer and cook uncovered for 20 minutes.
Remove the bay leaf.
Reduce the heat to low. Stir in the heavy cream, whole milk, soy sauce, and Worcestershire sauce. Heat gently without allowing the soup to boil.
Stir in the cooked wild rice and simmer gently for 5 minutes.
Remove the pot from the heat and stir in the lemon juice and 1 tablespoon of the parsley.
Taste and adjust with additional salt, pepper, or lemon juice if needed.
Garnish each bowl with the remaining parsley before serving.