Peel and finely chop the onion. Warm a pan over a low heat for 1 min. Add 1 tbsp oil and the onion. Season. Fry for 8 mins, stirring now and then.
Peel and finely chop the potato. Separate the celery sticks and trim the rough top and bottoms off them. Finely slice the sticks.
Add the potato and celery to the pan with a bay leaf. Season. Fry for 5 mins, stirring now and then.
Peel and quarter the apple. Slice out the apple cores. Roughly chop. Crumble the stock cube into a jug, add 800ml boiling water and stir. Add the apple and stock to the pan. Cover and bring to the boil. Simmer for 15-20 mins till the veg are very soft.
Tip the walnuts into a dry frying pan. Toast over a medium heat, shaking the pan, for 2-3 mins. Tip onto a board. Leave to cool, then roughly chop.
Remove the bay leaf. Ladle the soup into a blender and blitz until smooth, or use a hand-held blender in the pan. Taste and season. Serve topped with the walnuts.