Slice the leeks and wash them thoroughly in a bowl of cold water to remove any hidden dirt. Drain them well before you start cooking to ensure they sauté properly in the hot butter.

Melt the butter in your large saucepan over a medium-low heat setting. Add the sliced leeks and cook them slowly for about ten minutes until they are soft and translucent.

Stir in your diced potatoes and the chicken stock or water into the pot. Add the salt and bring the entire mixture to a gentle boil over a medium-high heat.

Reduce the heat to low and cover the pan with a tight-fitting lid. Let the soup simmer for about 30 to 40 minutes until the potatoes are very tender.

Use an immersion blender to puree the soup directly in the pot until it is completely smooth. If using a standard blender, work in small batches to avoid any hot splashes.

Pour the blended soup through a fine-mesh strainer into a large clean bowl. Press down with a spoon to catch any small bits for a perfectly silky French finish.

Cover the bowl with plastic wrap and place it in the refrigerator for at least four hours. The soup must be stone-cold before you add the final creamy ingredients.

Just before you are ready to serve, stir in the cold heavy cream. Start with half a cup and add more until the soup reaches your favorite creamy thickness.

Taste the cold soup and add more salt or white pepper if needed. Cold food often needs a little extra seasoning to make the flavors truly pop on your tongue.

Ladle the cold soup into chilled bowls and sprinkle fresh chopped chives on top. The green chives look beautiful against the snowy white color of the creamy potato soup.