I appreciate that what follows is unsolicited but I thought it might be helpful to capture and share the benefits of this broken stud extractor experience because I read very little on the tinterweb that turned out to be helpful.
This applies when the extractor (or Easy Out) is broken off inside the hole.
The good advice on the internet is you
can't readily drill a broken extractor! The advice I could not make work was Carbide or Cobalt drills which were reported to work on hardened material, which they do but with a lot of caveats. I suppose every scenario is different.

What did work for me:
- Grinding stones - cylindrical type
- Diamond grinders for Dremel type tool - used lots of water from a pressurised garden sprayer to lubricate
- Diamond cylindrical grinder - but wore out quickly, even lubricating as above
- Carbide spherical burrs
- Large, like 5.5mm carbide drill - cut away 2-3mm in 1hr approx
- Camera for close up pics to check what was really going on
Ironically, most of these successful tool bits were cheap.

What did not work for me:
- Tapping the extractor round with a punch to loosen it
- Trying to shatter the extractor
- Drilling with small carbide drills less than 3.5mm, just snapped
- Drilling round the side of the extractor into the "soft" stud
These were saviours because they lasted and didn't break. Use them in a Dremel type tool (I bought one for £15 off ebay)
Diamond spherical grinder - 1mm dia upwards. Readily available, often as engraving bits. I read that diamond bits clog in soft metal so kept it for working on the extractor.
Carbide spherical burr - 2mm dia upwards. Available from ebay seller glostertooling. These were excellent on the extractor and stud material. They didn't break in spite being small diameter. I did try a cylindrical or tapered carbide burr, it cut well but broke when it kicked back on a rough bit.
I mastered the right tools too late and with the material further down the hole it was increasingly challenging to do accurate work. If I had my time again (and I am not going to in a hurry!) I would:
- Try to loosen the extractor by knocking it clockwise with a hammer and punch on any rough bit left.
- Smooth the face with a cylindrical grinding stone just enough to control the next step.
- Use a 1.5 - 2mm diamond spherical grinder to cut a groove across the face of the extractor, deep enough for a screwdriver to gain purchase. Let the tool do the work, pressure will not help. Square off the profile of the slot with either a pointy diamond bit or a cylindrical bit so the screwdriver does not cam out so easily. Lubricate with plenty of water as you go. Allow 1 hour.
- Using a screwdriver bit no wider than the diameter of the extractor, try to reverse out the extractor. Worth investing the time here because it will still be quicker than "drilling out". I used the technique successfully a cm into the hole. It was beyond getting the extractor out but it loosened it enough for me to clear away the soft stud round the edge.
- Depending on the diameter of the extractor, try grinding away some of the stud around the circumference of the extractor. The carbide burr is good and will also cope with the extractor as well. I tried drilling with 1.5-2mm drills, even with HSS drills and they kept breaking. Remember to lubricate with oil.
- If the screw driver approach will not budge it and there is not enough stud between the extract and the hole's thread, then you are left with having to "drill out". You are now looking at up to 6 hours work. You will get there even though it does not feel like it.
- in a Dremel try a larger carbide spherical burr (oil lube) or diamond one (water lube)
- I found Carbide conical burrs partly successful but tended to kick back, eventually breaking. (Don't be tempted by adverts for a "recovery bit". It is basically one of these at 10x price.)
- Also small grinding stones in a Dremel make headway
- I lost favour with drills. The small tools above give lots of control but if you want to give it a go then use a diamond bit to grind a centre point for the drill. Drill with a 4.5 to 5.5mm carbide drill slow speed. Lots of lubricant. 1 hour = 2-3mm depth and 1 drill bit (£12+).
Although I thought I had preserved the thread quite well it did not look great when I cleaned it up with an M8 tap

I screwed a stud in as far as it would go (by hand) and backed it off a touch. It was much more wobbly than the other studs. Not wanting to risk the thread stripping I put in a thread recovery kit. Well worth the 20 mins.
Well known brand name is Helicoil. I used a Draper equivalent. At £20 from an agricultural place on Saturday morning it was much more expensive than on ebay.

This gave a lovely strong thread again.
... and Bongo is running quieter than ever now