In a large pot over medium heat, melt butter. Cook leeks in butter with salt and pepper until tender, stirring frequently, about 15 minutes.
Step 2
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.