In a large sturdy soup pot (or Dutch oven), melt the butter on medium heat. Cook the onions, carrots, potato, and garlic in the butter for 5 minutes, stirring occasionally. Add the chicken stock and pepper and bring the soup to a boil. Turn the heat down so that the soup is just barely bubbling. Cover the pot and cook the soup for 30 minutes.
Remove the soup from the heat and allow it to cool enough so you can comfortably puree it in a blender. Work in small batches and watch out for hot splashing soup! Once it is pureed return the soup to a pot. You can also puree this soup using a stainless steel food mill for a very smooth soup.
When you are done pureeing all the soup, stir in the whipping cream and season to taste with salt and additional pepper. You can further season this soup with such things as powdered dry ginger, cumin, and curry. All of these flavors go very nicely with carrots. I also like a pinch of cayenne.
Heat the soup to serve. Serve in bowls and garnish with chopped chives.
Makes about 4 - 1 1/2 cup servings.