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Melt the butter in a large saucepan over a low heat and tip in the onion, carrots and potato. Fry gently for about 10 minutes, stirring from time to time, until the onion is soft and the vegetables are glistening.
Pour in the stock and bring to the boil, then reduce the heat and partially cover the pan. Simmer for about 20 minutes, until the vegetables are soft.
Whizz the mixture in a food processor or blender until smooth (a blender will give a smoother texture), then add the cheese and whizz again. Return the soup to the pan, pour in the milk, then reheat gently and taste for seasoning. Serve the soup with buttered toast soldiers.