In a large pot or Dutch oven, heat 2 tablespoons of olive oil over medium heat. Add 1 pound of mixed mushrooms and 1 chopped yellow onion, cooking for about 15 minutes until the mushrooms are tender and the onions are translucent, stirring occasionally.

Once your mushroom and onion mixture is ready, lower the heat slightly and add 2 tablespoons of unsalted butter. Allow it to melt, then whisk in 2 tablespoons of all-purpose flour, 2 teaspoons of sweet paprika, and 1 tablespoon of chopped fresh dill. Cook this mixture for 1 minute, ensuring the flour is well incorporated.

Pour in ½ cup of dry white wine and stir vigorously to deglaze the pot, scraping any browned bits from the bottom. Allow the wine to evaporate for a couple of minutes until the alcohol is gone, then gradually whisk in 4 cups of low-sodium chicken or vegetable broth until fully combined.

Incorporate 2 tablespoons of low-sodium soy sauce and the sautéed mushroom mixture back into the soup. Bring the soup to a gentle simmer, and let it cook for about 5 minutes.

Lower the heat, and stir in 1 cup of whole milk and ½ cup of sour cream, mixing well until the soup is creamy and smooth. Bring the soup back to a gentle simmer while stirring frequently, then remove from heat.

Before serving, drizzle in 1 tablespoon of white wine vinegar or sherry vinegar, giving it a final stir. Taste the soup and adjust the seasoning with kosher salt and cracked black pepper as needed.