That's a good tip for MIG or stick.
With the TIG welder skip the washer and just weld a little pile on top of the broken bolt, even if it's broken off below the surface. Once the pile is tall enough to grab with vice grips give it a try. Sometimes on stubborn ones it'll take a few attempts. Part of why this works so well is the concentrated heat on the bolt alone.
I've used this method on screws as small as 6-32 and up to 5/8" so far, from broken off flush or just proud to well below the surface. Admittedly small ones below surface get a little tricky.
Grigg
