In a large saucepan over medium-high heat, melt the butter and saute the leeks until soft, about 3 to 5 minutes. Add the potatoes and stock and cook until the vegetables are cooked through and beginning to fall apart, about 15 to 20 minutes. If using an immersion blender, submerge in the soup and puree until smooth but with some small chunks remaining. *If using a blender, ladle the soup into the blender and blend until smooth but with some small chunks remaining. You may have to do this in 2 batches. Add the cream and blend to combine, then check for seasoning and add salt and pepper, to taste. Serve hot ladled into soup bowls and topped with some of the chopped chives.
*When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.