1. Begin by gathering and preparing all your ingredients, including washing and cutting vegetables and mushrooms.
2. Melt unsalted butter in a large saucepan or Dutch oven over medium heat until fully melted and bubbling.
3. Add diced onions to the melted butter and sauté until they soften and turn translucent.
4. Add mushrooms to the pot and sauté until they release their moisture and it evaporates.
5. Sprinkle flour and Hungarian paprika over the onion and mushroom mixture, stirring constantly to combine and form the soup’s base.
6. Gradually pour in the vegetable or chicken broth while stirring to create a smooth, consistent mixture.
7. Add soy sauce or liquid aminos and milk to the pot, stirring gently to combine.
8. Bring the mixture to a gentle boil, then reduce the heat to a simmer to allow the flavors to meld together.
9. Prepare a slurry using flour and milk in a small mixing bowl and gradually stir it into the soup to thicken it to your desired consistency.
10. Once the soup has thickened, turn off the heat and mix in sour cream or Greek yogurt.
11. Add fresh lemon juice, fresh or dried dill, and parsley into the pot, stirring gently to incorporate.
12. Taste and adjust seasonings according to your preference, including adding salt and pepper if needed.
13. Ladle the soup into serving bowls and garnish with freshly chopped parsley or an additional dollop of sour cream.
14. Serve hot with a slice of crusty bread or your favorite side dish.
15. For advanced variations, consider adding white wine, using mixed mushroom varieties, or incorporating other herbs like rosemary or thyme.