Bought the quadratec quick disconnect mirrors for riding with doors off. When trying to remove the stock bolts from the pillar, the fourth one stripped out and would not budge. I was mad as hell because I had my doors off already and was excited to hit the road for the first time topless and doorless. Then I remembered that I had a screw extractor set so I figured I would give that a whirl. Sure enough, I too broke one off...and it was now embedded in the head of the bolt. I didn't think to use heat, and glad I didn't as a previous poster noted it would hose up the paint. I was able to use a small screwdriver and hammer and work the extractor loose. I actually ended up using a smaller extractor than I originally thought I needed. Once you get the piece out (patience grasshopper, it will eventually come out!) here is what I would do (what worked for me):
1. use a drill bit that is the same size as the threaded part of the bolt, or slightly larger, and drill until the head pops off, leaving just the threads in the hole.
2. Using the "drilling" portion of your extractor, drill as deep into the body of the bolt as you can.
3. Jam the reverse threaded extractor side into this new hole as far as possible with some force and S-L-O-W-L-Y engage your impact driver to get it to bite.
Take your time, it will eventually work. BTW: I may have skipped a few steps in there that may or may not have involved lots of cursing a little bit of throwing things and a few kicks. Good luck, hope it works as well for you as it did me.