I do it all the time. The main thing is that once the stud has been broken off flush and drilling is the absolute last resort (don't ffs ever consider EZ outs).
File the stud so you are starting with a flat surface if possible. Take a good quality centre punch and punch a divot in the centre of the broken stud, this will stop the drill "wandering" when you start drilling. (top tip, take a paper towel and dip it in grease and put into the exhaust port, the swarf from drilling will stick to it and not drop down the port into the valve seat)
Start small with a 3mm drill and slowly drill into the stud and try to keep it absolutely straight. If you manage to keep it straight when you get to the 5 mm drill bit it will be possible to "wind out" what is left of the old thread of the original stud and then use a bottoming tap to clean up the threads before winding in a new stud.
If you have wandered off centre which happens to everyone, use a cutting tap to cut the new thread, then a bottoming tap to clean it out. (top tip, before use dip the tap in grease which helps lubricate the cut but also picks up all the metal swarf out of the hole). If the thread feels a little on the loose side then take the tap back out and refit with a coating of stud-lock.
If you have mucked the hole up or cannot be bothered to attempt to recover the original thread then an M6 Wire Thread Insert kit is the way to go, which involves drilling an oversized hole and taping it with an M7 thread and then winding in a insert (looks a bit like a spring) which then forms the replacement thread.