What was left of the old brake was cut off, and then the pieces that were still inside were carefully drilled out. The simplest solution would be to replace the broken brake with a pieces of dowel of appropriate size (perhaps with decorative knob?). We are discussing alternative solutions though that may lead to us not having to fix the same problem in the future. You have to love living in a household of engineers.
PS. I also wanted to make a quite shout out to my partner who has started a Photoblog chronicling his Project 365 participation. Not only does he do great machine working as evidenced above, but he is also handy with a camera. Actually he took the photo in this post as well.