Heat olive oil or butter in a large pot over medium heat.
Add the chopped onion and garlic and sauté until softened (about 5 minutes).
Stir in the sliced mushrooms and cook for about 10 minutes, until they release their moisture and begin to brown.
Add the thyme and broth, then bring to a simmer. Let cook for 10-15 minutes.
Stir in the cream and simmer for another 5 minutes. Season with salt and pepper to taste.
For a smoother texture, blend the soup using an immersion blender or regular blender (optional).
Serve hot, garnished with fresh parsley if desired.