If you are handy with a welder (MIG) that is the most effective way to get broken bolts out. I have just had to do it on my turbo housing Y pipe and the exhaust manifold. It is pretty simple. If the bolt is rusty, take a dremel or equivalent and clean the rust and dirt off. Then with a MIG welder spot a few times on the bolt to get a place to set the nut. I use a nut that is as large as can be fit. With pliers hold the nut over the spotted weld. Starting at the bottom on the spot weld in one steady motion fill the hole in the nut completely with weld. At this point the nut should be near white hot. You should wait til the nut has cooled to the point where it is dark (NO RED) Carefully spritz the area around the thread with PB Blaster. As soon as the welded nut cools to the point that the Blaster will stick to it, SOAK THE THREAD. Let it sit for a bit so you don't have to try and handle a hot part. Then with a wrench simply turn it out.
This method works wonders on old aluminum heads. The only time that you have to be extra careful is when the broken bolt is in a steel part. Then you just have to be more precise with the spot welding so you don't weld the broken bolt to the part.
I hope this helps.
