Man, if you have a broken bolt and it still has expose threads...Try the double nut method first.
Dont even try anything else but some kind of penatrating liquid ie Liquid wrench, WD-40 or what ever you can get a hold of
and no, massage oil will not work, or the heated oil...hahaha
on a serious note. I tried with a help of my friend (AF Metals Tech) and the help of the hobbie shop staff (old school Mech.)
we tried every little trick, such as- vice grip, bolt grabbers, this tool that grab the bolt as you tighten it, tapping the bolt and wrenching it. We even considered the torch method, but could not because of Air Force rules pertaining to Open flames and welding on a vehical with gas tank attached. (we tried to convince them that a motorcycle is not a vehical and I could take the tank in 3mins...they was not convinced.)
so we wasted like three hrs with no result...
left the hobbie shop and went to Checkers to pick up a pack of 7mm nuts. Went back today and tried the double nut...it did not take but 10 min to take out the two broken bolts and another bolt that was rusted but not broken. I wasted two weeks of ride time on something that took me 10 mins.
Knowledge/expericence comes with trial and error.

 

I didn't know you had threads exposed -- head of the bolt must've broken flush with the header. Anyway, good-frikkin-deal!!! Like I said before, anti-seize is your friend -- use it when reinstalling the header.

 

yeap, I've been told that I was really lucky to break both of them at the headers...
man, when I reassembled the headers I put more than enought of the antisieze on them,
just for assurance...Overkill, but owell