The most depressing sight !

[Uniboy]

Just got back from removing my rusty exhaust bolts, to come across the most depressing sight ever... After removing 7 of the little blighters one decided to hang on in there for the team... Bas$&^d

So now I need to fetch my mates stud extractor...

On the plus side my down pipes are now nice and shiny

 

[macem29]

on the bright side, there's some stud protruding to deal with...
a steel stud broken off flush in an aluminum housing is a way bad deal

 

[FinalImpact]

Bummer!

This would be a case where I'd do 3 things all at once as my first attempt to get it out.

1) take brass drift and hammer and smack the end of the stud to induce some shock to the threads and help break the bond sticking it in the head.
2) heat it with a propane torch
3) tighten it before you try to loosen it

If it remains stubborn, tapping on the boss where it resides could also be helpful to break the bond. You ride year round and are the roads salted or chemically treated? It looks like some form of corrosion is being mean to your bike.

You can try using two nuts back to back as jamb nuts. Vice grips or an actual stud extractor. Some penatrating oil might be good with several doses and overnight soaking too. . .

best of luck.