In a large pot, melt the butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and sliced mushrooms to the pot. Cook for about 8-10 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Sprinkle the flour over the mushroom mixture (if using) and stir to combine. Cook for an additional 2 minutes.
Pour in the vegetable broth, and add the thyme, salt, and pepper. Bring the mixture to a simmer and cook for 15 minutes.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you prefer a chunkier texture, blend only half of the soup and leave the rest as is.
Return the pot to low heat, stir in the heavy cream, and warm through for about 5 minutes. Adjust seasoning if necessary.
Serve hot, garnished with fresh parsley.