In a large pot, heat 2 tablespoons of olive oil over medium heat. Add 1½ pounds of sliced mixed mushrooms and 2 cups of diced yellow onions. Stir frequently until the mushrooms soften and shrink, about 15 minutes.

Remove the sautéed mushroom and onion mixture from the pot. In the same pot, melt 3 tablespoons of unsalted butter over medium heat. Whisk in ¼ cup of all-purpose flour, 4 teaspoons of sweet paprika, and 1 tablespoon of fresh dill. Cook the roux for about 1 minute.

Pour in ½ cup of dry white wine, stirring to deglaze the pot. Cook for about 2 minutes until mostly evaporated.

Gradually pour in 3 cups of low-sodium chicken or vegetable broth, whisking continuously. Bring to a gentle simmer, allowing it to thicken slightly, which should take about 5 minutes.

Stir back in the reserved mushroom and onion mixture along with 2 tablespoons of low-sodium soy sauce. Let everything simmer together for about 5 more minutes.

Lower the heat and whisk in 1½ cups of whole milk and ¾ cup of sour cream. Simmer gently for 3–5 minutes to ensure everything is heated through.

Remove from heat and stir in 2 tablespoons of white wine or sherry vinegar. Adjust seasoning as necessary, and serve hot, garnished with chopped fresh parsley.