In a stock pot heat the olive oil over medium heat. Add the chopped leek, onion, and garlic. Let it all cook, stirring frequently, until the veggies start to soften, about five minutes or so. Add the mushrooms and continue to cook everything for another 3-4 minutes, or until the mushrooms have started to brown. Pour the stock into the pot add the fresh thyme sprigs, and bring the pot to a simmer. Let the soup simmer for about 15-20 minutes.

Remove the thyme stems from the pot and discard. Using an immersion blender, puree the soup until it's smooth. If you need to use a stand blender, carefully blend the soup in batches and then return it back to the pot. Stir in the salt, pepper, and heavy cream. Adjust the seasoning, if necessary. Garnish with the chopped parsley and serve.