Melt the butter in a large pot over medium heat. Add the diced onion and sliced mushrooms once the butter begins to bubble.
Cook for about 8 minutes, stirring occasionally, until the onion becomes soft and translucent and the mushrooms release much of their moisture.
Pour in 2 cups of the vegetable stock. Add the dill, thyme, sweet paprika, Worcestershire sauce, salt, and ½ tablespoon lemon juice. Stir well.
Increase the heat and bring the mixture to a gentle boil. Reduce the heat to low and simmer for approximately 10 minutes, stirring occasionally, so the flavors have time to develop.
In a small bowl, whisk the remaining ½ cup vegetable stock with the flour until completely smooth and free of lumps. Whisk in the whole milk.
Slowly pour the milk mixture into the soup while stirring constantly. Continue cooking over low to medium-low heat for about 10 minutes, stirring occasionally, until the soup becomes creamy and slightly thickened.
Remove the pot from the heat. Allow it to cool for a minute or two, then stir in the sour cream and remaining 1 tablespoon lemon juice until smooth. This gives the Hungarian Mushroom Soup its signature creamy, lightly tangy finish.
Ladle into serving bowls. Finish each portion with a small spoonful of sour cream, chopped parsley, and freshly cracked black pepper.