Removing broken bolts are part of how i make my living. I'm a welder.

This is an 04 ford V8 exhaust.

When I weld a nut to the broken stud in this case, it heats the stud.

With heat, the stud wants to expand in all ways. It cannot expand in diameter because its contained.
It can grow in length. When it cools it contracts in all ways, so it sometimes breaks loose from the heat/cool action. This also makes the hole warmer so it expands. The nut welded on the end gives me a good hold.

Here are the many attempts it took me to get a stud out of a 1988 Suzuki 600 something. Lots of attempts but in the end I won.

I started out with a 110v mig welder. No joy so we hoisted the whole bike up by the front wheel and used TIG with 316LSI filler. After only a few more tries I got the stud out as seen in the pic.