Peel the potatoes, cut into chunks and boil until just cooked. Drain and allow to steam.
Meanwhile trim the tough ends from the leeks, cut in half lengthways, wash out any grit and slice thinly.
Heat the butter and when sizzling, fry the leeks for about 10 minutes until soft but not coloured.
Add the potatoes and stock or water and bring to the boil. Season with salt and pepper, reduce the heat and simmer for 20 minutes.
Add the parsley. Use a hand blender or food processor to blend the soup briefly - it should still have some texture.
Taste again for seasoning and serve hot.