1. Begin by thoroughly cleaning the mushrooms and slicing them evenly.
2. In a large pot over medium heat, add olive oil and butter. Once melted, add onions and shallots, seasoning lightly with salt and pepper.
3. Sauté the onions and shallots until translucent, then increase the heat slightly and add the sliced mushrooms.
4. Continue cooking the mushrooms until they release their juices and begin to caramelize, which takes about 7-10 minutes.
5. Pour in the white wine, deglazing the pot by stirring to lift any flavorful bits from the bottom. Allow the wine to reduce by half.
6. Add the broth of your choice (vegetable or chicken) and bring the mixture to a gentle simmer.
7. Insert fresh rosemary and any additional herbs, such as thyme or dill, to infuse the soup with herbal flavors.
8. In a small bowl, mix the milk or cream with the flour to prevent lumps, then slowly incorporate this mixture into the soup while stirring continuously.
9. Add Hungarian sweet paprika to enhance the soup’s flavor and vibrancy, and adjust salt and pepper according to your preference.
10. Lower the heat and let the soup simmer gently for 20-30 minutes to allow the flavors to meld.
11. If using optional ingredients like potatoes, add them at this stage and simmer until they are tender.
12. Check the soup’s consistency and seasoning before serving, making any final flavor adjustments as necessary.
13. Remove the rosemary sprig and any large herb pieces before ladling the soup into bowls.
14. Garnish each serving with fresh herbs or a small dollop of crème fraîche for an elegant touch.
15. Serve the soup alongside crusty bread or herby rolls for a perfect pairing and a comforting dining experience.