depending on how tight it was in there, getting the base out may be very tricky. If it wasnt too tight, try this first if there is no threads still sticking out. If it broke off fresh and clean, take a center punch and put a good dent in the rod in the the edge. Take a hammer and try and punch that around (counter clockwise) and maybe it will spin out. Sorry, its hard for me to clarify what im explaining without being able to show you. If not, you might have to drill it out a bit, and take an easy-out and try to get it out with that.

Its crazy that it just broke off. I constantly mess with all my stabilizers and have never had one break.
Derek