Grab a large saucepan and melt the butter over medium heat.
Add the leeks and cook over low heat, stirring a few times until they are softened (about 10-12 minutes).
Add the quartered potatoes, chicken stock, and the bay leaf to the leek mixture.
Season with salt and pepper. Bring the mixture to a boil, then turn the heat down and let it simmer for about 15 minutes.
Remove the bay leaf and discard it.
Transfer the leek mixture to a blender or use an immersion tool, and blend until smooth.
Grab a clean pot and return the leek mixture to the new pot.
Mash the potatoes in the bowl separately, or the potatoes become a gluey texture.
Add the potatoes back to the leek mixture.
Over medium heat, whisk in the heavy cream to the soup mixture and bring it back to a simmer, stirring constantly.
Add additional salt and pepper to taste if needed. Add snipped green onions and grated cheese as a garnish.