Melt the butter in a large saucepan over medium heat. Add the chopped leeks and garlic, then cook until softened (approximately 2-3 minutes). Add the mushrooms. Cook, stirring, for 2 minutes. Pour in the vegetable stock and bring to the boil.
Reduce the heat to low, then simmer, stirring regularly for 6 minutes or until the mushrooms are tender. Pour in the milk and cook for a further 5 minutes.
Allow to cool slightly, then blend until smooth. Place the cornflour into a small bowl. Add 1 tablespoon of the soup into the bowl with cornflour and continue to add an additional 5 tablespoons of soup while continually whisking. Return the soup to the saucepan over low heat. Whisk while adding the cornflour thickened soup slowly into the hot soup. Cook until the soup has thickened slightly.
Ladle mushroom soup evenly among serving bowls. Sprinkle with thyme leaves and serve with crusty bread – buon appetito.