I've been working on bikes for a few years and have never run into this problem until now.  I broke two spark plugs off trying to remove them.  Never seen, or let alone done that before.  I probably should have used some heat trying to remove them but I noticed on one that the rust had started to eat into the threads so it probably would have broken anyway.  I'll add a couple of pictures for everyone to see.
So, what is the consensus on removing broken spark plugs?    ugg, I think I know .... (remove engine, remove head, machine shop, drill out, tidy up threads, rebuild engine.)   ...  but, has anyone had luck doing it themselves/their selves without going the "full rebuild" route?