Jim, it makes a difference how it broke. If it were mine I would put
vise grips on it GOOD AND TIGHT and try to turn it gently. The threads
may not be very tight. But if they are, don't turn hard or risk further
screwing things up by chewing up the HANDY part that is now sticking out.
Like Don says, a stud puller is a great idea.
For example if you broke the headbolt torquing it, you can probably unscrew
it easily. If it has rust around it, not likely.
I've had broken ones that I was able to unscrew with my fingers.

This is one of the reasons that I make sure that both the bolt and the
hole are very clean, and I grease the threads also, for 2 reasons. One is to
make sure the torque is gainfully employed in advancing the threads, not just
twisting the shank of the bolt, so the bolt is loaded more in tension and
less in torsion, giving increased clamping force.
The second reason is for the benefit of whoever tears it down next - to keep
coolant and other crud, combustion products, etc from getting in the threads
and aggravating the motion when you go to unscrew it.
--
George Downs, The "original" Walrus3, Bartlesville, Oklahoma