In a large pot, melt the butter over medium heat. Add the chopped onion and minced garlic, cooking until the onion is translucent and fragrant (about 3-4 minutes).

Add the sliced mushrooms to the pot, stirring occasionally until they release their moisture and begin to brown (about 5-7 minutes).

Sprinkle the flour over the mushroom mixture, stirring to combine. Cook for an additional 2 minutes, allowing the flour to cook slightly.

Gradually pour in the vegetable broth, stirring continuously to prevent lumps. Bring the mixture to a gentle boil.

Reduce the heat to low and stir in the milk or cream. Add the dried thyme, paprika, salt, and pepper. Let the soup simmer for 15-20 minutes, stirring occasionally until it thickens.

Taste and adjust the seasoning if necessary. If you like a creamier texture, use an immersion blender to puree part of the soup, leaving some chunks for texture.

Ladle the soup into bowls and garnish with fresh parsley. Enjoy warm!