Peel and chop the potatoes. Wash the leeks, roughly chop them and put them in a saucepan with the potatoes, the onion, salt, pepper and the water. Boil and let cook for 40-45 minutes.
Blend the soup to a creamy consistency. Add one tablespoon of olive oil and mix well.
Pour the soup into 4 bowls. Add a little chopped parsley and a few pomegranate seeds to decorate.