Heat olive oil in a large pot over medium heat. Add onion and garlic, cooking until softened.
Stir in mushrooms and cook until they release their juices and brown slightly.
Add vegetable broth and dried thyme, then bring to a boil. Reduce heat and simmer for 15 minutes.
Blend half of the soup using an immersion blender or in batches in a blender. Return to the pot.
Stir in heavy cream and lemon zest. Season with salt and pepper to taste.
Simmer for 5 more minutes, then serve warm, garnished with parsley.