Insert the proper size REPS Extractor straight into the pipe, so that all four points "bite" at the same time. Turn the extractor counter-clockwise with a wrench, and the pipe will unscrew on its own threads.
Drill a hole* in the exact center of the broken part deep enough for the REPS Extractor to achieve its shallow grip. Insert the proper size extractor straight into the drilled hole, so that all four points "bite" at the same time. Turn the extractor counter-clockwise with a wrench, and the stud or screw will unscrew on its own threads.
* Walton provides a chart of recommended drill sizes for each extractor size.