Sorry, I must have skipped over the word broken - I can see now that you did mention that. My recommendations would be one of the following options, A, B, or C:
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A1) Disconnect the caliper from the banjo-bolt - clamp the brake hose with a pair needled vice grips with rubber lining on their teeth.
A2) Take the caliper to a bench to work on.
A3) Heat the caliper up around the area of the bleeder valve - avoid heating the valve itself.
A4) As it's cooling, use a washer and nut to weld on the (cleaned) bleeder valve end.
A5) Take an impact gun to the newly-welded nut.
A6) When it breaks off the valve, clean the area and start again. Repeat with the impact gun.
A7) This is the most sure-fire way of getting it out, however it requires the most equipment. If this is not a possibility for you - see Option B. If the valve becomes irremovable - or the caliper threads destroyed - see Option C.
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B1) Buy a bolt extractor kit at your local tool store. Set the caliper on a bench and secure in a vice, like before.
B2) Pre-drill a small hole - perfectly centered - within the bleeder screw. Do not let it drill off-center.
B3) Heat the caliper up around the area of the bleeder valve - avoid heating the valve itself. Let the caliper cool a bit before proceeding.
B3) Use the appropriately-sized extractor bit in your drill, and set to reverse (it is a reverse-threaded drill bit, which cuts into the valve's/bolt's/whatever's center and turns it out.) Too big of a bit and you'll just annihilated the valve, aim smaller.
B4) When it fails (it likely will) - see Option C. When the bolt extractor breaks inside the f%&#ing valve, demand your money back from the store you bought it at - and see Option C.
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C1) Buy a new caliper (with new valve included) at your local parts store, and exchange the old one with the broken valve for the core charge.
C2) Open a beer and ask yourself why you didn't just choose Option C in the first place.
In all seriousness, that situation leaves you with few creative options. Your vice grips will NEVER remove that broken valve if a six-point socket failed. That's the plain truth.
-Dubya