I recently went through this exercise with a broken bolt on the U-bracket on my front sway bar.
I used a punch to place a small dent in the center of the broken bolt (correctly centering that dent is extremely important), and then I used a set a high quality set of drill bits, starting with the 1/16" bit, and drilled a hole through the center of entire length of the broken bolt. I then repeated the drilling process for each and every larger size drill bit in my set, until I used a drill bit that was slightly smaller than the diameter on the bolt (so as not to cut into the threads of the threaded portion of the hole on the frame.
Then I used a small cold chisel to collapse inward the remaining shell of the broken bolt, thus breaking the lock on the threads. Once the broken bolt was loose, I used a pair of needle nose pliers to back the broken bolt shell out. Last, I used a tap with the correct diameter and thread to clean out the threaded hole on the frame.
The entire process took about 2 hours. I wish you success on removing your broken bolt.