In a large pot over medium heat, melt butter. Cook leeks in butter with salt and pepper until tender, stirring frequently, about 15 minutes.
Stir cornstarch into broth and pour broth into pot. Add the potatoes and bring to a boil. Season with salt and pepper. Pour in the cream, reduce heat and simmer at least 30 minutes, until potatoes are tender. Season with salt and pepper before serving.