Sauté the mushrooms: Heat olive oil in a large pot over medium heat. Add the sliced mushrooms and cook until they release their juices and turn golden brown, about 8-10 minutes. Remove half of the mushrooms and set aside for garnish.

Cook the aromatics: In the same pot, melt the butter. Add the chopped onion and cook until translucent, about 5 minutes. Stir in the minced garlic and thyme, cooking for another minute until fragrant.

Make the roux: Sprinkle the flour over the onion mixture and stir well to combine. Cook for 2 minutes to remove the raw flour taste.

Add the broth: Gradually pour in the vegetable or chicken broth while stirring constantly to avoid lumps. Bring the mixture to a simmer.

Blend the soup: Use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup to a blender in batches and blend until smooth, then return to the pot.

Finish with cream: Stir in the heavy cream and reserved mushrooms. Simmer for another 5 minutes. Season with salt and black pepper to taste.

Serve: Ladle the soup into bowls. Garnish with fresh parsley and a drizzle of cream if desired.