Bring a saucepan of water to the boil and add the potatoes. Boil for 10 minutes and then add the onions and celery. Boil for a further 5 minutes until the potatoes are tender.
Drain off the water and return the potato mixture to the stove over a gentle heat.
Remove any rind from the cheese and crumble into the potatoes, stirring until melted.
Sprinkle over the chopped parsley and walnut halves. Serve immediately with a green salad.