I'm making this soup right now It's very yummy. I made it to great acclaim last year when I had my friends over for corned beef and cabbage.
→[More:]It's a lot less unhealthy than the standard variations of potato soup, too, since it uses broth instead of cream (well, I used cartons of stock instead of broth).
I don't know why they call it irish, though. I thought potato leek soup was traditionally a french thing...