Heat the oil in a large saucepan over medium heat. Add your leeks and cook for 5 minutes. Then, add your mushrooms and thyme and cook for 8 more minutes. Finally, stir in the flour and cook for 1 additional minute.
Add the vegetable stock and bring the soup to a boil, then lower the heat and simmer for 10 minutes.
Puree the soup using a heat-proof blender or an immersion blender until smooth. Then add the milk and wine, and simmer for an additional 5 minutes, or until the soup is heated through.
Notes
Recommended low FODMAP Surving Size – 1 cup per sitting