Melt the butter in a large, heavy-bottomed pot or Dutch oven over medium heat. Add the diced onions and cook, stirring, for 3 to 4 minutes until softened and translucent. Add the sliced mushrooms and cook for 5 minutes, stirring occasionally, until they release their liquid and begin to brown.

Stir in the dried dill, Hungarian paprika, soy sauce, and vegetable broth. Reduce the heat to medium-low, cover, and let the soup gently simmer for 15 minutes.

In a small bowl, whisk together the cornstarch and whole milk until smooth. Pour the mixture into the soup, stirring constantly until well incorporated. Cover again and continue to simmer very gently for another 10 minutes, stirring occasionally to prevent sticking.

Remove the pot from the heat. Stir in the sour cream, lemon juice, chopped parsley, salt, pepper, and a pinch of cayenne if using.

Return the pot to low heat and cook for 3 minutes, just until heated through. Do not let the soup boil, or it may curdle.

Ladle the soup into bowls. Garnish each serving with sautéed mushrooms, a dollop of sour cream, and a sprinkle of fresh parsley. Serve immediately with crusty sourdough bread.