Heat the oil in a 6 quart pot over medium heat. Add the leeks and potatoes. Sauté until softened, 5 to 10 minutes.
Add the parsley, broth, salt and pepper, and nutmeg (optional). Bring to a boil. Reduce the heat to low and simmer the contents, covered, 40 minutes, until tender. Serve the soup as is or process in a blender.
Serve warm or chilled. Adjust seasoning before serving.
Note: White pepper is recommended for appearance in white soups. However, freshly ground black pepper is recommended for taste.