Heat oil in a large saucepan over medium heat. Add the onion, garlic and thyme, cook, stirring for 5 minutes until the onion is soft. Add the potato and cook for 5 minutes until potato starts to soften.
Increase heat to high, add the mushrooms and cook for 5 minutes. Add 5 cups of stock and bring to the boil. Reduce heat to medium and boil gently, stirring occasionally, for 10 minutes.
Blend or process to desired consistency. Return soup to clean pan and stir in the cream if using. Season with salt and pepper, adding remaining stock to adjust the consistency if required. Cook over medium-low heat (without boiling) until warmed through.
Ladle the soup into warm serving bowls or cups, sprinkle with thyme and serve with toasted rye bread.