Prepare vegetables: Chop the carrots, parsnip, or celeriac into small cubes. Chop the onions and the garlic finely.

Cook: Pour the vegetable broth or chicken stock into a soup pot. Add the prepared vegetables, bring to a boil and cook until they are soft, about 15 minutes.
In the meantime, wipe the mushrooms clean with some kitchen paper and slice them.

Saute mushrooms: Heat half of the butter in a large pan, add the sliced mushrooms and the thyme and cook until the mushrooms are golden, stirring several times in between, about 5 minutes. Remove ⅓ of the mushrooms and set them aside. Discard the thyme sprigs.

Thicken: Push the remaining mushrooms to one side of the pan. Melt the remaining butter in this empty space, sprinkle the flour over the butter, and let it get very slightly golden. Slowly start adding about 1 cup from the soup while whisking all the time to avoid getting clumps. When the mixture is smooth, stir to coat the mushrooms with it. If it is too thick, you can add a bit more of the soup. Continue cooking for another 2 or 3 minutes. Add the mushroom mixture to the soup.

Blend: Add the milk and the cream cheese and blend the soup very thoroughly with an immersion blender. Heat through again but don't let it boil anymore.

Finish: Add the reserved mushrooms and adjust the taste with salt and pepper.
Sprinkle the soup with parsley and serve immediately as suggested above.