[Dragncar]

Since being a millwright I deal with broken bolts on a regular basis. The kids I train these day come to me with broken bolts and studs.
A few things. 6 point sockets only. Ff its a Allen, and particularly a flat head Allen which many times will have a smaller socket, always have a sharp Allen wrench/socket, dig out all the debris and make sure its seated all the way before even trying. Because once you strip it, you have two problems, not one.
Sometimes you can make a poor mans impact with a breaker bar and socket with another guy hitting the back of the breaker bar with a hammer while you apply torque.
A good penetrate oil is your friend. (not WD40) Left handed drill bits are also your friend. A small carbide bit that also cuts on the end is useful for making a flat spot for your center punch if the bolt/stud is broken below the surface at a angle.
Heat can be your friend but also hurt you if you get your steps out of order. You can heat the female side and give it a shot. But I only heat in a half circle, not all the way around. If I heat a nut, its only one flat.
With a Allen head you can heat it and hit it with water cooling quickly and that will shrink the fit and make it tighter on your wrench/socket if its partially stripped. It also pulls the metal away, makes some room if that is what is making it grab. Particularly with flat head Allen's.
If you are planning on drilling it out do not heat and cool anything because if its a grade 8 bolt(all Allens are), you are not drilling anything out at that point. Hard as can be. Even if you did have a hole a Easy Out will not grab. Grade 5 bolts do not harden nearly as much when you heat-cool them.
If some of the bolt is sticking up, even a tiny bit you can sort of plug weld a washer to what is left then weld a nut to the washer and back it out. As long as you do not heat and quench drilling out is still a option if this does not work.
The final is the fire wrench. A cutting torch. If I can get a 1/4" hole drilled through a broken bolt in a non blind situation I can cut it out and leave the treads. You make the hole a little bigger with the torch and the heat makes it bigger. Then you quench and it gets smaller. Do it a few times and it might get loose enough so it will back out.
If it will not you carefully keep making it bigger, then cool. When you get near the female threads you max cool it with water. When is left of your hollowed out broken bolt will be thin and heat quickly. The female part will be cold enough that when you hit the oxygen they will not go away, only your bolt will. Clean up with tapper tap.
If it is a large, short broken bolt in a blind hole you can start cutting a little hole in the center, cool, repeat. You will make a little reverse cone hole, eat a lot of fire in the face so be prepared but after a few cycles many times it loosens and you can stick a large flat bladed screwdriver in what is left and back it out.
Took years you learn this the hard way. Now I passed it on.