Remove a broken bolt.

One way I often use to remove a broken bolt that has broken off flush is to lay a washer with center hole diameter that is slightly smaller than the bolt on top of the broken bolt. Then weld the washer and broken bolt together at the center hole, place an appropriate sized nut on top of the washer and weld the washer and nut together through the center of the nut. After it cools a bit, I can usually just use a wrench to unscrew the bolt.