[Carnut427]

Welcome to Club Cobra.
jarendall's method will work, but you may have to use a Boron drill bit. I'd try using a pick like an ice pick or something else that's slim and sharp on the end to try and wiggle the broken part out first if you haven't tried that. You might also be able to hit it with a center punch opposite the direction you were turning the tool when it broke to jar the broken part loose. If you can use a pair of Vise Grip pliers or a pipe wrench to remove the bolt first, it might be easier. However, I'm going to guess you were trying to remove the bolt when the star tool broke, so the bolt may be too tight for that to work. Another possibility is the tool you used was a cheap one; when you buy another to replace the one that broke, make sure it is high quality, such as Craftsman, SK Tools, Lisle, Mac etc.
On a problem like you have, you try several different ways until you succeed.