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). I sprayed plenty of PB Blaster into the drill hole after each bit went through the entire length of the bolt shell.
Then I used a small cold chisel to collapse inward one side of 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.