Peel the sweet potatoes and cut them into small pieces.
Heat the chicken stock. When it is simmering, add the sweet potatoes, return the liquid to a simmer, and cook until the sweet potatoes are very soft. At this point, salt the soup carefully to taste. (See Kitchen Notes.)
Cool the soup. You may decant it in a bowl if you wish, or move the pot into the refrigerator, but it is essential to cool the soup thoroughly at this point. Once it is well cooled (see Kitchen Notes), process it in a blender or food processor until it is uniformly smooth and rather thick. Work in batches if you need to.
Once the soup is entirely puréed, pour it into a large container, cover and refrigerate until you are ready to serve it. You can make it up to a day ahead. At the point when you are about to serve the soup, stir in the cream.
Ladle the cold soup into individual bowls. Choose a bowl that will show off the pretty pale-coral color of the soup. As you see from the photo, we use pink Manhattan glass bowls. Simple white ones or clear glass bowls would be beautiful too. Garnish with the chives or scallions, and serve.
Homemade Chicken Stock
Here's how to make the homemade chicken stock, the key to the success of the vichyssoise. Makes about 20 cups of stock---you can freeze what you don't use right away.
To prepare the chicken, first rinse it well under hot water. Then cut off and discard as much fat as you feel like bothering with. Put the chicken in a 16-quart pot.
Add the carrots, onions, whole peppercorns and parsnip. Fill with cold water to cover everything amply. Do not add salt at any point!
Bring to a boil, then reduce the heat to simmering. Skim off the foam and discard it. Simmer gently until the chicken is beyond useful—it should be falling off the bones.
Taste it to be sure it is chickeny enough. The flavor should assert itself even without salt (which you have not added, yes?). Turn off the heat. Remove all the solids from the stock—I set a colander over a big bowl or over a pot and drop the solids into the colander. Press down on the solids with the back of a big, heavy spoon. Then discard the solids. Anything that has drained into the pot below should be added back to the stockpot.
At this point, when the stock has been off heat for a little while, you can separate the fat if you wish—I like the OXO Good Grips Fat Separator for handling this work when the liquid is still hot. Or you can ladle the still-fatty stock into individual storage containers. Cover them, cool in the refrigerator; then, when the stock has cooled, if you need to hold the stock over for a few weeks, move the containers into the freezer. It is easier to scrape off the fat during the thawing process than to separate it from the hot stock.