Just got through doing this fix this weekend. Had the same stud broken off as shown in the image above, but mine was broken clean with the head. Let me just say if you are going to attempt this yourself and have no other option but to drill the stud out, make SURE you drill directly in the center of the bolt. I center punched the bolt but didn't leave a good enough indent, so when I started drilling I ended up off center. Rather than stop and reset, I figured I'd just get it done with and TRUST ME when I say this was a terrible idea. Quick fix turned into a major headache.
I'd also recommend drilling with left handed drill bits right from the start, as this may make the use of easy outs redundant. Really it shouldn't be that bad of a job, and if you have the tools and are handy don't be scared of doing it to save some money. Just be careful and take your time. If anyone has questions about the experience feel free to PM me and I'll do my best to help out.