Melt the butter and saute the leeks and garlic about 10 minutes, until very soft. Stir it all up frequently and keep the heat low enough so the garlic doesn't brown.

Add everything else except the milk and bring to a boil, then lower the heat. Cover and simmer for 20 minutes, stirring now and then. Basically, you just want to make sure the potatoes are cooked. If you like, blend parts of the soup in the blender or using a handheld mixer, but you can skip this step and just have chunkier soup. When the soup has cooled just a bit, add the milk or cream, stir and serve.

This soup is just as good cold--at which point you can call it Vichyssoise.