Melt the butter: In a heavy pot over medium heat, melt 4 tbsp of unsalted butter. Once melted, add the 1 large finely chopped onion and sauté until it becomes soft and translucent, about 5 minutes.
Add the mushrooms: Incorporate 1 lb of thinly sliced mushrooms into the pot. Stir to combine, cooking them for another 5 minutes. This step helps release their natural juices.
Add the broth and seasonings: Pour in 2 cups of chicken broth along with 1 tbsp of soy sauce, 1 tbsp of sweet Hungarian paprika, and 2 tsp of dried dill weed. Bring the mixture to a gentle simmer and let it cook for 15 minutes. This time allows the flavors to meld beautifully.
Thicken the soup: In a separate bowl, whisk together 1 cup of whole milk and 3 tbsp of all-purpose flour until smooth. Gradually stir this mixture into the soup, mixing continuously for about 15 minutes or until the soup thickens to your desired creamy consistency.
Finish with sour cream: Reduce the heat, and gently fold in the ½ cup of sour cream, 3 tbsp of chopped parsley, 2 tsp of lemon juice, and salt and pepper to taste. Heat through without letting the soup boil, approximately 3-5 minutes.
Serve: Ladle the soup into bowls, garnish with additional parsley, and serve warm alongside crusty bread for a fulfilling meal.