Cobber

Here in Oz we call that a shouldered bolt.
To get the broken threaded piece is easier said than done!
I just spent the last 2 weeks removing broken high tensile bolts from a large plastics shredder for a recycler. The machine is getting a thorough overhaul having spent the last 10 years running 24/7.

The best and most reliable method I've used is as follows:
I use a pneumatic die grinder with a carbide burr to grind the uneven breakage smooth (you could use a dremmel instead of a die grinder), this will allow me to use a center punch to put a punch dimple in the center of the broken bolt now using a small cobalt drill bit (@ 3mm or 1/8") in a pneumatic drill ( a good battery drill will do) I drill a pilot hole through the center of the broken bolt.
Next I use a lefthanded drill bit a size or 2 smaller than the bolt diameter...... as you drill in the drill should bite as it cuts into the bolt this will unscrew the broken bolt from the hole.( of course you use a left handed drill in reverse) If this doesn't work then I use a drill bit of the size that you would use to tap the thread ( example to cut an 8mm dia thread you would dill a 6.5mm hole, there are reading charts on the net to give you a guide as which drill size to use on the required tread tap)
I now carfully retap the thread to remove the old tread coils.
Should the tread be to damaged to repair by retaping I use a thread insert such as a helicoil or recoil brand.
But it is absolutely essential that you drill you hole in the center of the bolt.......get it off center and your in a world of pain!

There are various broken bolt removers out there such as the easy-out but you still need to drill the center of the bolt.... get it wrong and you'll break the east-out, you should NEVER EVER use an open-ender spanner or adjustable wrench to turn an easy-out, use a tapping wrench.


A better and more modern bold extraction tool is from a company called Alden, they make a tool called a Grabit Drillout, that is a cross between a left handed drill bit and an easy-out........ yet again you need to drill your hole in the center. And read the bloody instructions!


There are other so called methods out there but unless you get lucky they will probably cause more harm then good.....remember I do this for a living!