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 potatoes and place them in a bowl and set them aside. Remove the bay leaf and discard it. Transfer the leek mixture to a blender, 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.