Use a torch like real muff men do.
WTF does a torch do for you if your dealing with a broken off bolt?
Ever hear of a cutting torch? Guess you haven't.
Again though.
What is a cutting torch going to do for you?
It's designed to cut metal so how does that help?
You dont want to cut off whats remaining of the bolt if you're lucky enough to have anything left sticking out and if for some insane reason you wanted to you damn sure wouldnt use a cutting torch.
Like Sunni said,if you have something hanging out the last thing you wanna do is cut it off.
Now if you have a little to work with you weld a nut or bolt to it and the heat from the welding is plenty to loosen things up.
I've removed thousands of broken taps,drills and bolts from parts over my 30 years as a machinist.
In a lot of cases an EDM is required if the part is expensive and the drill,bolt or tap is really hard because a drill will walk off the hard material and track to the softer material.
You can use an end mill to flatten the broken off part to help with drill walking but that goes out the window when talking about carbide drills and taps or Grade 8 bolts.
Dont try and school me on anything related to metal work.
I'm sure to embarass you.