Add the virgin oil in a large pan and add the chopped leeks. Fry them over a low to medium heat until the leeks are soft. Stir frequently so that none of the ingredients brown.
Add the chopped potatoes and chicken broth to the pot.
Bring the soup to the boil and then let it simmer (just barely boiling) for the remaining cooking time.
Cook for 15 to 20 minutes until the potato is soft.
Use a masher or a blender to break down the potatoes in the pan.
Just before serving, pour the heavy cream into the soup and stir well.