Melt the butter in a large saucepan. Add the leek, cover and cook over a low heat for 5 minutes. Add 2 tablespoons of water and cook gently for 10 more minutes. Pour the stock over the leek, stir, then cover and continue to cook gently for 10 minutes.
Put aside a few peas for garnish, then tip the rest into the pan. Add the sugar and heat for 5 minutes, without boiling. Allow the mixture to cool slightly, then tip into a blender or food processor and purée until smooth. Season to taste. Return to the pan and reheat gently.
Pour the soup into four bowls and add a swirl of cream and a few of the reserved peas to each one.