+1 to the above. If it has snapped it is because the manifold has warped. (They are most likely all going to do it eventually, mine had not been remapped and it was very badly warped. Only one snapped is actually quite lucky, a lot of us have had more than one go, me included, I lost at least 2, cannot actually remember.
So get it off, get it skimmed, cut through the webs for good measure, drill out the outer two holes on each end by 2 mm further and the next two in (numbers 2 and 4) by 1 mm. That should prevent it happening again.
Then go to the head and if the rest of the stud is still there you may be able to, very carefully, get it out. provided there is enough of it left to get a grip on with tons of freeing-off liquid, stud extractor, etc, etc. But don't expect it to be easy.
If it has snapped off below the surface of the ehad then you'll need to drill it out and retap it as you said. You may even have to redrill it a size bigger and tap that hole, then fit a corresponding stud/cut off bolt. The you'll need to drill out the manifold hole even wider.
Don't be surprised if some of the studs try to come out with the nuts, you could snap even more off. Go very gently and use lots of WD or whatever.
There are quite a few threads on this on here and I sincerely wish you a lot of luck as it can go horribly wrong.