That happened to me awhile back.
I raised the rear of the mower up on a hoist so as to be easy to get at the twisted off rusty brake bolt.
Steel bolt going into aluminum. Severely galled threads.
Just slightly enough stub to get vise grips onto then took vise grips off, took a propane torch (could have used oxy/acyt but did not want that much heat)
and heated the aluminum housing around under the bolt stub, not excessive heating, just a good warming to expand the aluminum and took a hammer and pecked several times on the stub of the bolt. (was really lucky that it left little bit of a stub)
This heat helps break up the galled steel/aluminum around the threads. Heat peck try to wiggle. (patience)
Finally got a slight movement but still lots of pecking and wiggling.
Finally got it to come out but still had to go back and forth several times all the way out. I could have tried welding a nut onto the stub but I wanted to actually see the stub bolt itself as I was trying to turn.
I chased the threads on both and used anti-seize during assembly.
Probably took at least 30 min's just warming and pecking on the stub. (knowing that if I twisted off it would result in a bad thing)