Trim the roots and about 3cm off the top of the leek. Slice a cross into the top of the leek and open it out. Rinse out the grit. Finely slice it.
Warm a pan over a medium heat for 2 mins. Add 1 tbsp oil and the leek. Season with a pinch of salt and pepper. Cover and sweat for 5 mins.
While the veg sweat, trim the dry ends off the celery sticks and finely slice them. Peel and dice the potatoes. Peel and crush the garlic. After 5 mins, stir the chopped veg and garlic into the pan. Cover and sweat for a further 5 mins to soften the veg up.
Crumble the stock cube into the pan. Pour in 700ml boiling water. Cover, bring to the boil, then simmer for 10 mins.
While the soup simmers, tip the walnuts into a dry frying pan. Toast for 2 mins, shaking the pan, till they're toasted and smell nutty. Tip onto a chopping board. Let them cool for a few mins, then roughly chop them.
Use a hand-held blender to blitz the soup in the pan, or ladle it into a blender and blitz till smooth. Taste and add a little more salt or pepper if needed.
Ladle the soup into warm bowls. Top with the toasted chopped walnuts and serve.