Heat the oil in a large saucepan and add the onion, celery and leek. Fry for about 5 mins until softened.
Add the potatoes and stir to prevent them sticking, then add the sweetcorn. Stir in the flour and cook for 1 min, then add the milk and stock, stirring all the time. Bring to the boil, then reduce the heat and simmer gently for about 15 mins until the potatoes are softened. Stir in the cheese and sprinkle over the chopped parsley.
For very young babies, blitz the soup in a blender until smooth. For older babies, simply blitz half the soup and mix with the remainder to give a textured purée.