I had to extract one of those broken studs early on in my Morgan life. They are very brittle and one snapped off flush with the bodywork.
First I stuck a washer around the stud with double sided tape to protect the paint.
Then over the next few evenings (still working then) I used a pin chuck (finger drill) to drill down the stud until I got sawdust.
Then I tapped in a triangular needle file and the broken stud wound out easily with pliers.
